s3. · pdf fileiv acknowledgements i would like to thank my supervising professors dr. gary a...
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Copyright
by
Gholamreza Garmeh
2005
Simulation of Interwell Gas Tracer Test
in Naturally Fractured Reservoirs
by
Gholamreza Garmeh, B.S
Thesis
Presented to the faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in Engineering
The University of Texas at Austin
August 2005
Simulation of Interwell Gas Tracer Test
in Naturally Fractured Reservoirs
Approved by:
Supervising Committee:
Kamy Sepehrnoori
Gary A. Pope
iv
Acknowledgements
I would like to thank my supervising professors Dr. Gary A Pope and Dr. Kamy
Sepehrnoori for their supervision and guidance throughout the course of the work.
They shared with me their knowledge, experience and insight, which encouraged and
enlightened me to pursue the art and science of research.
I would like to thank Dr. Mojdeh Delshad for her valuable advice. Thanks to Joanna
for helping me with all the software and hardware problems and thanks to Esther for
all her help. I would like to thank Kaz and Elif for their help in getting started on my
research. My special thanks go to Vicencio, Farhad and Yousef for their helpful guide
in reservoir simulations. I would like to acknowledge NIOC for financial support of
this course of study.
It has been a highly rewarding experience to pursue graduate studies at The
University of Texas at Austin, and I am thankful to the people who have helped and
guided me during the course of my study.
I need to thank CMG company for all their software support.
Finally, thanks go to my family and friends for their encouragement throughout my
stay at the University of Texas at Austin.
v
Abstract
Simulation of Interwell Gas Tracer Test
in Naturally Fractured Reservoirs
by
Gholamreza Garmeh, M.S.E
The University of Texas at Austin, 2005
SUPERVISORS: Gary A. Pope and Kamy Sepehrnoori
The main objective of this research was to investigate the gas tracer test in naturally
fractured reservoirs and compare the dual porosity and discrete fracture models for
the gas tracer test. The method of moments was used to estimate the average oil
saturation and swept pore volume in naturally fractured reservoir gas tracer tests. It
was used to estimate mobile oil saturation for a case of uniform residual oil saturation
in the matrix and fracture, and for a case of different residual oil saturation in the
matrix and fracture from total concentration of the produced tracer. Results verify that
the method of moments is a fast, simple, and accurate method of estimating the oil
saturation in fractured reservoirs. The gas tracer test in naturally fractured reservoirs
was simulated for the dual porosity and discrete fracture models and results were
vi
compared. Results of the ECLIPSE simulator were compared with the IMEX
simulator for the dual porosity and discrete fracture models. The comparison
demonstrates that the discrete facture model has properties of the dual porosity model
and the reality of a fractured reservoir. In addition, the effect of dimensionless groups
in the dual porosity and discrete fracture models were studied. The effect of
dimensionless parameters in the fracture tracer transport was analyzed and the
equilibrium condition of the gas tracer’s transport between the matrix and fracture
was obtained.
vii
Table of Contents
Acknowledgements.....................................................................................................iv
Abstract.........................................................................................................................v
Table of Contents.......................................................................................................vii
List of Tables...............................................................................................................xi
List of Figures...........................................................................................................xiii
CHAPTER 1:
Introduction..................................................................................................................1
CHAPTER 2: Literature Review...............................................................................4
2.1 Tracer tests in oil fields............................................................................................4
2.1.1 Application of tracer test in oil fields.............................................................4
2.1.2 Tracer tests in fractured reservoirs..................................................................5
2.1.3 Development of oil field tracer technology....................................................7
2.1.4 Tracer interpretation methods.........................................................................8
2.1.4.1 Method of moments..........................................................................10
2.1.4.2 Inverse modeling...............................................................................15
2.2 Application of gas tracers for reservoir characterization…...................................18
2.3 Fractured reservoirs...............................................................................................20
2.3.1 Dual porosity model.....................................................................................21
2.3.2 Discrete fracture model................................................................................22
2.4 Review of the Cantarell oil field............................................................................24
viii
CHAPTER 3: Use of gas tracers for reservoir characterization. .........................30
3.1 Partition coefficient for gas tracers........................................................................30
3.2 Estimation of gas tracer partitioning coefficient…..............................................32
3.3 Simulation of tracer flow in slimtube…................................................................33
3.4 Simulation of gas tracers in fractured reservoir.....................................................36
3.4.1 Reservoir Parameters and geology data for base case simulation...........36
3.4.2 Base case simulation with dual porosity model......................................38
3.4.3 Results.....................................................................................................39
3.5 Estimation of oil saturation and swept pore volume using method of moments.39
3.5.1 Method of moments for dual porosity Model. ..........................................40
3.5.2 Estimation of mobile oil saturation in dual porosity model. .....................42
3.5.3 Estimation of oil saturation in dual porosity model with different residual
oil saturation in the matrix and fracture. ...................................................43
3.6 Conclusion..........................................................................................................44
CHAPTER 4: Comparison of discrete fracture and dual porosity models for
gas tracer injection.............................................................................57
4.1 Driving forces in fractured reservoirs....................................................................57
4.2 Shape Factor study.................................................................................................59
4.3 Base case simulation for dual porosity and discrete fracture models. ..................61
4.4 Dual porosity model...............................................................................................62
4.4.1 Simulation of fractures by dual porosity model. ....................................62
4.4.1.1 Relative permeability tables in fractured reservoirs................62
4.4.1.2 Capillary pressure in naturally fractured reservoirs.................63
4.4.2 Simulation of fractures by dual porosity model in ECLIPSE and
IMEX........................................................................................65
4.4.3 Subgridding. ...............................................................................66
ix
4.5 Simulation of gas tracers by tracing a component in GEM...................................67
4.5.1 Simulation in dual porosity media. ........................................................67
4.5.2 Comparison of tracer test between ECLIPSE and GEM........................68
4.6 Simulation of fractures by modeling the fractures as discrete fracture network...68
4.6.1 Problem to model fractures as discrete fracture......................................69
4.6.2 Discrete fracture model...........................................................................69
4.6.3 Grid refinement.................................... ..................................................70
4.7 Simulation of fractures by modeling the fractures as Equivalent single porosity.71
4.8 Conclusion.............................................................................................................71
CHAPTER 5: Application of dimensionless groups to naturally fractured
reservoirs..........................................................................................94
5.1 Gravity Number Ng...............................................................................................94
5.1.1 Effect of Ng on oil recovery in dual porosity model……….......................95
5.1.2 Effect of Ng on oil recovery in discrete fracture model…………..............95
5.2 Effective length to thickness ratio. ........................................................................96
5.2.1 Effect of LR on oil recovery in the dual porosity model. ...........................96
5.2.2 Effect of LR on oil recovery in the discrete fracture model. .....................97
5.3 Dimensionless groups for fractures tracer transport..............................................97
5.3.1 Mean residence time in fractured reservoirs................................................98
5.3.2 Sensitivity analysis for dimensionless parameters of tracer transport.........99
5.3.2.1 Matrix number..............................................................................100
5.3.2.2 Fracture porosity. ........................................................................101
5.3.2.3 Matrix to fracture porosity...........................................................102
5.4 Conclusion...........................................................................................................104
x
CHAPTER 6: Summary, Conclusions and Recommendations for Future Work
6.1 Use of gas tracers for reservoir characterization..................................................118
6.2 Naturally fractured reservoirs model...................................................................119
6.3 Dimensionless groups study................................................................................120
6.4 Dimensionless groups in fractured reservoir tracer transport…..........................120
6.5 Recommendations for future work......................................................................121
Appendix A: Sample input files
A.1 ECLIPSE Input File for 3 phases flow of tracer test.....................................123
A.2 ECLIPSE Input File for dual porosity model.................................................132
A.3 ECLIPSE Input File for discrete fracture model.............................................140
A.4 CMG-IMEX Input File for dual porosity model.............................................158
A.5 CMG-IMEX Input File for discrete fracture model........................................164
A.6 CMG-GEM Input File for component tracking as tracer in dual porosity media.
........................................................................................................................181
Nomenclature...........................................................................................................189
References ................................................................................................................195
VITA.........................................................................................................................209
xi
List of Tables
Table 2.1: Cantarell formation test 1 Data (Lopez and Gonzalez 2001………...…....28
Table 2.2: Cantarell formation test 2 Data (Lopez and Gonzalez 2001)………...…..28
Table 3.1: Property of selected tracers (Maroongroge 1994)………………………..46
Table 3.2: Fluid composition for estimating tracer partitioning coefficient………....46
Table 3.3: Equilibrium ratio and partitioning coefficient of the selected tracers at
reservoir condition……..……………………….......................................46
Table 3.4: Partitioning coefficient and relative Retention volume for slimtube
displacement…………………………………………………………........47
Table 3.5: Data for simulation of slimtube displacement (Maroongoge 1994).……..47
Table 4.1: Reservoir data for dual Porosity model simulation………………...….…73
Table 4.2: Relative permeability and capillary pressure date for case 1……..……...73
Table 4.3: Relative permeability and capillary pressure data for case 2……...…..…75
Table 4.4: Relative permeability and capillary pressure data for case 3……...…..…75
Table 4.5: Reservoir data for discrete fracture model simulation……………...…….75
Table 5.1: primary parameters value for Scaling group analysis……………...……106
Table 5.2: Summarized data for Ng in dual porosity model…………………..……106
Table 5.3: Summarized data for effect of Ng in discrete fracture model……..……106
Table 5.4: Summarized data for effect of LR in dual porosity model………...……107
xii
Table 5.5: Summarized data for effect of LR in discrete fracture model……..……107
Table 5.6: Base Case Data for simulation of dimensionless parameter in fractured
reservoir………..………………………………………………………..107
Table 5.7: Summarized parameters values for different MaN …………..…………108
Table 5.8: summarized parameter values for case of different fφ ……..………….108
Table 5.9: summarized parameter values for case of different Sgf
mφφ …..…………109
xiii
List of Figures
Fig. 2.1: Location of Cantarell oil field (Limon-Hernandez et al. 2005)……...……29
Fig 3.1: Comparison between produced tracer concentration history of Slimtube
Experiment with ECLIPSE simulation results…..…………………….……48
Fig 3.2 Normalized tracer concentration for dual porosity simulation case…………48
Fig 3.3 Oil production rate for dual porosity simulation case………………….……49
Fig 3.4 Oil Recovery for dual porosity model simulation……………………...……49
Fig 3.5: Tracer concentration at the producer for dual porosity model (Semi-Log
scale)…………………..……………………………………………....……50
Fig. 3.6: Tracer Concentration at the producer for dual porosity model……….……50
Fig. 3.7: Tracers recovery for different partition coefficient in dual porosity media..51
Fig. 3.8: Oil saturation estimation from Method of moments in dual porosity media
with mobile oil……….……………………………………………….……51
Fig. 3.9: Sweep efficiency estimation from Method of moments in dual porosity
media with mobile oil……….………………………………………..……52
Fig. 3.10: Tracer production concentration at the producer for different residual oil
saturation in matrix and fracture (Semi-Log scale)……..…...……..……52
Fig. 3.11: Tracer production concentration at the producer for different residual oil
saturation in matrix and fracture…...……………………………..………53
Fig. 3.12: Conservative tracer concentration profile in layer 3 after 50 days of tracer
xiv
injection……………………………………………………………………..……….53
Fig 3.13: Conservative tracer profile in layer 3 after 250 days……………...………54
Fig. 3.14: Conservative tracer profile in layer 8 after 250 days……………..………54
Fig. 3.15: Conservative tracer profile in layer 9 after 250 days……………..………55
Fig. 3.16: Oil saturation estimation from Method of moments in dual porosity media
for different residual oil saturation in matrix and fracture………….……55
Fig. 3.17: Sweep efficiency estimation from Method of moments in dual porosity
media for different residual oil saturation in matrix and fracture…..……56
Fig 3.18: Tracers recovery for different partition coefficients in dual porosity media
for different residual oil saturation in matrix and fracture….…...………56
Fig. 4.1 Typical fractured reservoir model…………………………………..………75
Fig. 4.2: Relative permeability curve for matrix system contain gas and oil..………75
Fig. 4.3: Relative permeability curve for fracture system contain gas-oil…...…..…76
Fig. 4.4: Matrix oil saturation profile before gas injection in simulation case...…….76
Fig. 4.5: Matrix oil saturation after 2000 days of gas injection for case1……...……77
Fig. 4.6: Oil production rate and oil recovery for case 1……………………….……77
Fig. 4.7: Matrix capillary pressure for gas-oil system in case 2……………..……78
Fig.4.8: Oil production rate and Oil recovery efficiency for case 2…………...….…78
Fig 4.9: Matrix oil saturation after 2000 days gas injection for case 2………...…….79
Fig. 4.10: Matrix capillary pressure for gas-oil system in case 3……………...……79
xv
Fig. 4.11: Oil production rate and oil recovery efficiency for case 3…………..……80
Fig. 4.12: Matrix oil saturation after 2000 days of gas injection for case 3…...…….80
Fig. 4.13: Oil production rate in ECLIPSE and IMEX for dual porosity model.……81
Fig. 4.14: Horizontal nested subgrided matrix block in ECLIPSE (Eclipse Manual
2004)…………….………………………………………………………..81
Fig. 4.15: Schematic view of concentric subgrided matrix blocks in ECLIPSE (Sinha,
2004)…………………………..…………………………………...…….82
Fig. 4.16: Oil production rate for subgrided model and dual porosity model in
ECLIPSE……….,.…………………………………………………...…...82
Fig. 4.17: Oil Recovery Efficiency for subgrided model and dual porosity model in
ECLIPSE…………………………..………………………………..……83
Fig. 4.18: Oil production rate for subgrided model and dual porosity model in
IMEX…………..…………………………………………………….…..83
Fig. 4.19: Oil Recovery Efficiency for subgrided model and dual porosity model in
ECLIPSE………………...……………………………………………..…84
Fig. 4.20: Oil production rate comparison between ECLIPSE and GEM………...…84
Fig. 4.21: Comparison of tracer test in ECLIPSE and component tracing in GEM…85
Fig. 4.22: Mole fraction (N2B) in fracture after 50 days………………………….…85
Fig. 4.23: Mole fraction (N2B) in matrix after 50 days……………………………...86
Fig. 4.24: Mole fraction of (N2B) in fracture after 200 days…………………….….86
Fig. 4.25: Mole fraction of (N2B) in matrix after 200 days………………………....87
xvi
Fig. 4.26: Tracer concentration profile in fracture after 50 days in ECLIPSE………87
Fig. 4.27: Tracer concentration profile in matrix after 50 days in ECLIPSE………..88
Fig. 4.28: Tracer concentration profile in fracture after 200 days in ECLIPSE……..88
Fig. 4.29: Tracer concentration profile in matrix after 200 days in ECLIPSE………89
Fig. 4.30: Oil Production rate in dual porosity model and discrete fracture model…89
Fig. 4.31: Oil Recovery Efficiency in dual porosity model and discrete fracture
model……………………………………………………………………..90
Fig. 4.32: Conservative tracer response in dual porosity model and discrete fracture
model…………..……………………………………………………..…..90
Fig. 4.33: Partitioning tracer response in dual porosity model and discrete fracture
model………………………………………………………………….….91
Fig. 4.34: Oil production rate for discrete fracture model in ECLIPSE and IMEX…91
Fig. 4.35: Local Grid Refinement for discrete fracture model…………………...….92
Fig. 4.36: Oil production rate for discrete fracture model and LGR……………...…92
Fig. 4.37: Oil production rate comparison in dual porosity, discrete fracture and
equivalent single porosity models………………….…………………….93
Fig. 4.38: Cumulative oil production rate in dual porosity model and equivalent single
porosity model…………………………..………………………..…...…93
Fig. 5.1: Effect of Ng on oil Recovery efficiency at LR =20 for dual porosity model…109
Fig. 5.2: Effect of Ng on oil recovery efficiency at LR =10 for discrete fracture
model............................................................................................................109
xvii
Fig. 5.3: Effect of LR on oil recovery at constant Ng=0.02949 for dual porosity
model............................................................................................................110
Fig. 5.4: Effect of LR on oil recovery efficiency at Ng=0.02949 and for discrete
fracture model……….……………………………………………………110
Fig. 5.5: Effect of MaN on Mean residence time of tracer
response…………………………………………………………………..111
Fig. 5.6: Effect of MaN on conservative tracer response…………………………...111
Fig. 5.7: Effect of MaN on conservative tracer response in Semi-Log scale...……..112
Fig. 5.8: Effect of fφ on output tracer response at MaN =0.02……………………112
Fig. 5.9: Effect of fφ on output tracer response at MaN =0.02 (Semi-Log scale)....113
Fig. 5.10: Effect of fφ on output tracer response at MaN =20.0…………………..113
Fig. 5.11: Effect of fφ on output tracer response at MaN =20.0 (Semi-Log scale)...114
Fig. 5.12: Effect of Sgf
mφφ on Mean Residence Time at MaN =0.02……………….114
Fig. 5.13: Effect of Sgf
mφφ on Tracer response curve at MaN =0.02………………..115
Fig. 5.14: Effect of Sgf
mφφ on Tracer response curve at MaN =0.02 (Semi-Log
scale).........................................................................................................115
Fig. 5.15: Effect of Sgf
mφφ on Mean Residence Time at MaN =20.0……………….116
xviii
Fig. 5.16: Effect of Sgf
mφφ on Tracer response curve at MaN =20.0……………….116
Fig. 5.17: Effect of Sgf
mφφ on Tracer response curve at MaN =20.0 (Semi-Log
scale)........................................................................................................117
1
CHAPTER 1: Introduction
Fluid flow in naturally fractured reservoirs has gained more attention because
of its complex process. In fractured reservoir, flow is primarily through the high
permeability fractures, and matrix blocks contain the majority of the reservoir pore
volume and act as a source or sink to the fractures. A lot of work has been done to
model fluid flow through fractured reservoirs. The dual porosity model can handle
naturally fractured reservoir performance. In this model, two sets of properties are
specified: matrix porosity and permeability, and fracture porosity and permeability. In
the dual porosity model fluid flows only in fractures.
The discrete fracture model has many of advantages of dual porosity model plus
reality of the fractured reservoir complex. In the discrete fracture model, fractures can
be modeled based on well log, seismic data, coring, and well test data.
The partitioning interwell tracer test is a powerful tool to characterize reservoir
properties such as estimation of oil saturation, evaluation of sweep efficiency,
detection of flow barrier, flow channeling and flow pattern, identifying reservoir
heterogeneity and reservoir layering.
The study in this research focuses on simulation of gas tracer tests in fractured
reservoirs to estimate average oil saturation, swept pore volume, and to compare the
dual porosity model and discrete fracture model for gas tracer test.
2
Chapter 2 presents the review of previous work done in application of tracer
test in oil fields. It reviews application of gas tracers in oil fields and presents the
various methods that have been used to estimate reservoir oil saturation and evaluate
sweep efficiency. It also reviews the work done to model fractured reservoirs as a
dual porosity and discrete fracture models. Furthermore, it presents geology and
reservoir property of the Cantarell oil field which is a naturally fractured reservoir. Its
reservoir properties have been used in our simulation studies.
Chapter 3 presents a gas tracer test for reservoir characterization. It starts with
the definition of the partition coefficient in gas tracers. Partitioning coefficient has
been estimated by equation of state for perfluorocarbons gas tracer. The accuracy of
the simulator was tested to simulate gas tracer test by introducing an experimental
tracer test to compare the results. In this chapter we also apply the method of
moments to estimate mobile oil saturation in a naturally fractured reservoir using a
dual porosity model.
Chapter 4 compares simulation of the gas tracer test in naturally fractured
reservoirs using the dual porosity and discrete fracture models. The properties and
advantages of each model have been discussed and their results for production rate,
recovery efficiency and tracer transports have been presented. A compositional
simulator such as GEM was used to model gas tracer test by tracing a component of
injection gas as slug tracer. The results of simulations by ECLIPSE have been
compared by GEM to check the accuracy of the results.
3
Chapter 5 discusses the effect of dimensionless group on oil recovery in
fractured reservoirs. It compares results of dimensionless groups study for the dual
porosity model and discrete fracture model and subsequently analyzes sensitivity of
dimensionless parameters for fracture tracer transport.
Chapter 7 present summaries, conclusions and recommendations for future
work.
4
CHAPTER 2: Literature Review
This chapter reviews previous research that has been performed in the area of
partitioning interwell tracer tests to characterize oil field reservoirs. It reviews gas
tracers and their application in oil fields. Finally, it reviews the properties of naturally
fractured reservoirs and tracer tests in fractured reservoirs.
2.1 Tracer tests in oil fields
Tracers are used for many reasons and in a variety of circumstances. Tracers
are used to describe the reservoirs, investigate unexpected anomalies in flow, or to
verify suspected geological barriers (Zemel, 1995).
2.1.1 Application of tracer test in oil fields
Mercado and Perez (2003) used the tracer in a gas flooding project to
determine existence of flow channeling, to find flow barrier and flow pattern
direction, to evaluate sweep efficiency and magnitude of the injector and producer
communication, and to identify heterogeneity. Saad et al. (1988) applied the tracer to
study cross flow phenomena and reservoir layering. Allison (1991) used the tracer to
estimate residual oil saturation and sweep efficiency. Dugstad et al. (1999) applied
the tracer test to determine layering, channeling and evaluate WAG sweep efficiency.
Wagner (1977) found that following information could be obtained from every tracer
5
test: volumetric sweep efficiency, identification of the offending injector, directional
flow trend, delineation of flow barriers, and relative velocity of injected fluids.
A lot of work has been done to estimate residual oil saturation from tracer tests.
Wood et al. (1990) estimated residual oil saturation from tracer tests. Tang (1995)
introduced chromatographic transformation technique to estimate residual oil
saturation from partitioning interwell tracer tests (PITT). Tracers can also be used in
the test section of the field before expanding the flood (Zemel, 1995).
2.1.2 Tracer tests in fractured reservoirs
Tracer tests in fractured reservoirs have been recognized for its shortcomings
when applied to heterogeneous carbonate reservoirs. It shows the performance of
moderate dispersion, early arrival, long production tails and extreme dilution of tracer
profiles (Tang & Zhang 2001).
Tang and Zhang (2001) determined residual oil saturation in fractured reservoirs.
They used two different models: the dual porosity model, where the tracer could
distribute between the flowing and non-flowing pores through mass transfer, and a
single porosity model. The residual oil saturation was determined by simple analytical
models, including mass balance method, peak method and mean retention volume
method. The dual porosity model consisted of two parts of mass balance: tracer
transfer in flowing pores and tracer diffusion in dead-end pores.
6
Their model could handle the long tracer production tail caused by slow diffusion of
the tracer into and out of the dead-end pores.
Ramirez et al. (1993) analytically modeled the tracer flow in naturally fractured
reservoirs. The reservoir was treated as being composed of two regions: mobile
(fractures), where dispersion and convection take place, and stagnant (matrix), where
only diffusion and adsorption was allowed. Radioactive decay was considered on
both regions. The solutions were presented for linear flow of vertical fractures and
radial flow of horizontal fractures and cubic block matrix-fracture geometry. These
solutions accounted for all important mechanisms that affect tracer flow: diffusion,
convection, adsorption, and radioactive decay.
Shinta and Kazemi (1993) introduced an analytical and dynamic transfer function,
which was capable to reduce dual porosity model (DPM) into single porosity model
(SPM). They used their formulation in combination with tracer transport, to
characterize the reservoir fracture properties.
Grigorievich and Archer (1993) introduced a method for identification of residual oil
from the data of two tracers with different solubility in oil for the fractured porous
media. Their result of theoretical prediction of the tracer wave propagation was in
good agreement with the laboratory experiment’s data.
7
2.1.3 Development of oil field tracer technology
An ideal tracer test must accurately follow the path and velocity of the
carrying fluid and it must be easy to identify and measure quantitatively (Zemel,
1995).
Partitioning interwell tracers have been used to estimate None Aqueous Phase Liquid
(NAPL) saturation from the 1990’s. Pope et al. (1994) were the first to use and report
a PITT. According to the progress of tracers, Bingyu et al. (2002) divided tracers into
four generations. Chemical tracers were the first generation technology, applied in the
1950’s. It contains all kinds of inorganic saltines, stain and alcohol. Moreover, the
precision was about 10-4 ~ 10-6 (ppm) only.
Radioactive isotope tracers were the second generation technology, applied in the
1970’s. It includes tritiated water, tritiated alkane and tritiated alcohol. The purpose
of measurement was liquid phase scintillation counter, and the precision was up to
10-9 (ppm) level. The third generation of tracers was applied at the end of the 1980’s.
The significant characteristic was some stable isotope, which could be activated.
Microelement tracers were the fourth generation technology that has been applied
since the 1990’s; the basic principle was to take the matter that very little in the
formation water and reservoir fluid was applied as the tracer. The measurement
precision of this kind could reach up to the level of 10-15 (ppm).
8
2.1.4 Tracer interpretation methods
With development of computer technology, the application of tracer tests in
oil fields have been programmed by some interpretative software to interpret tracer
tests in oil fields. Interpretations include numerical methods, analytical methods, and
semi-analytical methods. Meanwhile the range of reservoir parameters interpreted
became wider with better precision. The interpretation methods are progressing to be
perfect. Recently, the methods, which interpret the produced tracer profile, combine
with the geological model (Bingyu et al. 2002).
Brigham and Smith (1965) for the first time developed some equations to predict the
time of tracer breakthrough, the peak concentration of tracer and the degree of
stratification in the five-spot pattern.
Cooke (1971) used the chromatographic method to determine residual oil saturation.
Deans and Majoros (1980) used the method of moments to estimate residual oil
saturation for a single well tracer test. Allison et al. (1991) introduced a method for
the interwell tracer test to estimate residual oil saturation, the mobile oil saturation
and sweep efficiency in the multi-well, multi-tracer project. Tang and Harker (1991)
used the landmark comparison to estimate residual oil saturation from a gas injection
in carbonate reservoir.
Maroongroge et al. (1995) developed the method of moments for estimation of
residual oil saturation and swept volume for water tracer test and the vertical tracer
profiling to stochastically model reservoirs. Zemel (1995) presents a comprehensive
9
study of oil field tracers to design and interpret tracer tests in oil fields. Dwarakanath
and Pope (1998) identified the various sources of error in both the measured PITT
and errors from data analysis of the method of moments that was used to estimate oil
saturation from PITTs.
Deeds et al. (1999) developed the method of moments for three phases and included
dispersion and diffusion, and variable saturations and porosity to it. He applied the
method of moments to analyze gas tracers in contaminated aquifers with non-aqueous
phase liquids. Tang and Zhang (2001) used the single well tracer test to determine
residual oil saturation by simple analytical models including mass balance method,
peak method, and mean retention volume method for single-porosity and double-
porosity models.
Jayanti (2003) analyzed the effect of the heterogeneity and detection limit on
partitioning interwell tracer tests.
Asakawa (2005) developed the method of moments for the three-dimensional
heterogeneous porous medium. He extended the derivation to include the calculation
of oil saturation in naturally fractured reservoirs and calculation of the oil saturations
for reservoirs with mobile oil from the total concentration of tracers in water and oil
phase.
Sinha et al. (2004) used natural tracers as a cost effective partitioning tracer to
calculate residual oil saturation. He used the method of moments for interpretation of
PITTs in heterogeneous reservoirs with spatially variable residual oil saturation.
10
Altinay (2005) combined method of moments (MOM) with inverse modeling to
obtain accurate and realistic oil saturation estimation from Partitioning interwell
tracer tests (PITT). She used method of moments in a complimentary way by using
oil saturation estimation from method of moments as an initial guess of inverse
modeling calculation.
More attention has been given to method of moments and inverse modeling to
estimate residual saturation from tracer tests in recent years.
2.1.4.1 Method of moments
Asakawa (2005) estimated the oil saturation and swept pore volume from the
zero and first temporal moment of produced tracer concentration.
His assumptions in the derivation for the case of tracer slug injected into a reservoir
are as follows:
• The partition coefficient of each tracer is constant during the test,
• Diffusion at the well boundaries is negligible,
• There is no mass transfer of tracers across the boundaries of the swept volume
of interest,
• Tracers are chemically stable during the test,
• There is no destruction or generation during tracer test,
The following equations are for slug gas tracer injection. Equations are analogous
with water tracers, except the tracer is partitioned into oil and gas instead of oil and
11
water. The mass conservation equation for thi tracer flowing in the reservoir is given
by
0NtC
ii =⋅∇+
∂φ∂ r
, (2.1)
where the total tracer concentration is
ij
n
1jji CSC
p
∑=
= , (2.2)
and for tracer flow through porous media:
∑=
∇⋅φ−=
pn
1jijijjjiji CKSuCN
rrrr (2.3)
For a tracer slug injection:
≥=
≤≤=
sluginjectorit
slugiJinjectorit
tt,0C
tt0,CC (2.4)
Multiplying Equation (2.1) by time and integrating over time gives:
0dtNtm0
ii0 =⋅∇+φ− ∫∞ r
, (2.5)
where
dtCm0
ii0 ∫∞
= (2.6)
Integrating Equation (2.5) over the reservoir volume of interest
12
0dVdtNtdVm0
ii0 =
⋅∇+φ− ∫∫∫ ∫∫∫∫
∞ r (2.7)
Applying divergence theorem to Eq. (2.7)
0dAndtNtdVm0
ii0 =⋅
+φ− ∫∫ ∫∫∫∫
∞rr
(2.8)
Since mass transfer occurs only at the wells, then
( ) 0qmdVm wellsi1i0 =+φ− ∫∫∫ , (2.9)
where
dtCftm0
n
1jijji1
p
∫ ∑∞
=
= (2.10)
This equation is the first moment and could be applied to a variety of water, oil and
gas combinations. For the specific case of oil and gas with no partitioning of tracers
into water, it can be written as follows:
( )
( )
( )( ) dVmSKS
dVdtCSKS
dVdtCSKS
dVdtCSCS
dVm
ig0oig
0igoig
ig0
oig
0iooigg
i0
∫∫∫ +φ=
∫∫∫ ∫+φ=
∫∫∫ ∫ +φ=
∫∫∫ ∫ +φ=
∫∫∫φ
∞
∞
∞
(2.11)
13
where the partition coefficient of tracer i is defined as
ig
ioi C
CK = (2.12)
and
dtC
dtCSS
0ig
0igj
j
∫
∫=
∞
∞
(2.13)
Equation (2.9) can be used to show that
( ) 0VmdVmSKS iproducerig0ig0oig =+∫∫∫ +φ− , (2.14)
where the mean residence volume of tracer i is given as
2V
dtC
dttqCV slug
0ig
0it
i −
∫
∫=
∞
∞
(2.15-1)
or mean residence time of tracer i :
2T
dtC
dttCT slug
0ig
0it
i −
∫
∫=
∞
∞
(2.15-2)
Assuming jS is not different between tracers and that ig0m is not a function of space,
it follows from Equation (2.14) that
( ) 0VdVSKS ioig =+∫∫∫ +φ− (2.16)
14
Equation (2.16) can be used to show that the average oil saturation in 3-Phase flow is:
)1()1(*)1(ˆ
2112
21−−−
−−=
KVKVVVSS wo (2.17)
And the swept pore volume is given by
21
2112 )1()1(*))1(
1(KK
KVKVS
Vw
s −−−−
−= , (2.18)
where the tracer is not partitioning into water phase.
The average oil saturation oS is at the mean residence time of the conservative
tracer 1t , therefore the average oil saturation at the end of the PITT is given by
subtracting the volume of oil produced after the mean residence time:
s
toos
o V
dtqSV
S 1∫∞
−
= (2.19)
After the mean residence volumes obtained, the swept pore volume between wells
and the average oil saturation in each swept pore volume can be calculated (Asakawa
2004). The retardation factor for partitioning tracer i is defined as follow:
or
orifi S1
SK1R
−+= (2.20)
15
2.1.4.2 Inverse Modeling
Recently, the streamline approach has received a lot of attention for
computing the sensitivity of parameters. With the streamline method, sensitivities can
be computed analytically using a single flow simulation (Cheng et al. 2004).
The streamline-based inversion approach is an analytical sensitivity computation
method that yields sensitivities of the partitioning tracer response to the porosity,
permeability and NAPL saturation in a single streamline simulation, and it uses
efficient techniques from the geophysical inversion to match the field tracer response
and estimate subsurface parameters. In this approach, the NAPL saturation estimation
is a two-step procedure: First, the conservative tracer response is matched to provide
permeability distribution then the partitioning tracer response is matched by varying
the NAPL saturation distribution in the subsurface (Yoon et al. 1999).
A streamline-based inverse model named TAMU was developed at Texas A&M
University (Vasco et al., 1999, Yoon et al., 1999, Datta Gupta et al, 2002).
Lliasov et al. (2001) used the TAMU inverse model to estimate the residual oil
saturation distribution in the Ranger field from the PITT data. Oyerinde (2004)
extended Lliasov’s derivations to estimate mobile oil saturation distributions using
the TAMU inverse model coupled with ECLIPSE to the multi-well PITT data from
the Ranger field.
16
Yoon et al. (1999) developed an approach, which decouples the flow and transport by
a coordinate transformation from the physical space to one following flow directions
versus the tracer time of flight along streamlines.
The time of flight is defined as:
∫=τ ψ dr)x(S (2.21)
Where ‘slowness’ is defined as follows:
)x(v1)x(S = (2.22)
The tracer transport along streamlines in terms of time of flight coordinates is given
by
0CtC
=τ∂
∂+
∂∂
(2.23)
The tracer concentration at the producer obtained by integrating the contributions of
individual streamlines (Datta-Gupta & King 1995).
∫ ψτ−= ψall 0 d)t(C)t(C (2.27)
0C is the tracer concentration at the injection well. For partitioning tracers, the travel
time along streamlines is increased in the presence of NAPL saturation. This can be
expressed in terms of an increased slowness as follows:
)SKS()x(v
1)x(S oow += (2.24)
17
oK is the partitioning coefficient of the tracer defined as the ratio of tracer
concentration in oil phase to that in water phase.
Finally, Darcy’s law for velocity is introduced into the equation:
)SKS()x(p)x(k
)x()x(S oow +∇
µφ= (2.25)
The next step is the sensitivity computation of the tracer response with respect to the
model parameters such as permeability, porosity and NAPL saturation. The
streamline-based method has been selected to compute sensitivities (Yoon et al. 1999).
Consider a small perturbation in subsurface property around an initial model:
)x(S)x(S)x(S 0 δ+= (2.26)
)t,x(C)t,x(C)t,x(C 0 δ+= (2.27)
Assume that streamlines do not shift as a result of a small perturbation. Then the
tracer time of flight and concentration has the following relation to the slowness:
∫ δ=δτ ψ dr)x(S)x( (2.28)
∫ δτ−−=δψ
dr)x(S)t(C)t,x(C '0 (2.29)
Slowness variation will be given by
δs(x) = +δ∂
∂ )x(kk
)x(S
φ∂∂ )x(S δ φ (x) + Sw
Sw)x(S
δ∂∂ , (2.30)
where the partial derivatives are
18
)KoSoSw(p)x(k)x(
k)x(S
2 +∇
µφ−=
∂∂
(2.31)
)koSoSw(p)x(k
)x(S+
∇µ
=φ∂
∂ (2.32)
)Ko1(p)x(k)x(
Sw)x(S
−∇
µφ=
∂∂
(2.33)
Note that in the above expressions, the pressure changes have been ignored because
of small variations in the permeability. For the unit partitioning coefficient, the tracer
response will be insensitive to saturation changes. The tracer travel time and
concentration sensitivities with respect to the permeability, porosity, and water
saturation can be obtained by integrating Equation (2.28) and Equation (2.29) over all
streamlines contributing to a producer (Yoon et al. 1999).
The NAPL saturation estimation based on the partitioning tracer response is a two-
step procedure: First, the conservative tracer response is inverted to estimate spatial
distribution of the permeability, and then this permeability distribution is applied to
invert the partitioning tracer response to estimate oil saturation distribution.
2.2 Application of gas tracers for reservoir characterization
The major difference between gas and water tracer tests is the phase in which
tracers reflect as mobile fluid. For this case, we assume that retention is only by the oil
phase. The retardation factor is defined as (Brusseau et al. 2003):
19
)SS1(KS
1Rwo
ogo
−−+= , (2.34)
where Kog is the oil–gas partition coefficient and Sw is water saturation. Tang and
Harker (1991) were the first to introduce gas-phase partitioning tracer tests to
determine residual oil saturation. Many gas tracer tests have been conducted for
reservoir characterization. In 1969, gas injection with radioactive gas tracers on East
Coalinga field, California, was carried out to determine the reservoir continuity. Gas
tracer surveys were carried out successfully and at the end of the injection period,
tracer response was detected from 11 producing wells. The test showed generally
better continuity than that inferred from the outcrop study for reservoir
characterization (Tinker 1973).
In 1998, a gas injection with a gas tracer program was planned to be carried out in EI
Furrial field. The main goal of this tracer injection was to establish the path of gas
movement through the reservoir, and according to the gas tracer test, the geological
model was revised and the main direction of the fault was changed, because the fluid
movement in the reservoir had a dramatically different tendency compared with the
previous model (Vilela et al. 1999).
Radke and Gillis (1990) developed the analytical model to determine the trapped gas
saturation during steady state foam flow by the dual gas tracer injection. Effluent
concentration of tracers was influenced by solubility of each tracer on the liquid
20
phase. The measured tracer histories were fit to a simple mass transfer model that
describes any partitioning between mobile and trapped foam.
For direct calculation of the residual oil saturation from tracer data Tang (2002) has
proposed three different forms of chromatographic transformation, namely landmark
comparison, equal recovery, and equal normalized recovery. Tang and Harker (1991)
used a landmark comparison relationship (Equation 2.35) to estimate the residual oil
saturation from a gas flood at the Golden Spike carbonate reservoir:
max,p
p
max,n
nC
)(CC
)t(C τ= , (2.35)
)1(t β+=τ , (2.36)
g
org
HSS
=β (2.37)
Equation (2.35) shows that, the partitioning to a non-partitioning tracer is equal to the
delay factor (1+ β ). Therefore, by comparing the corresponding landmarks on the
non-partitioning and partitioning tracer curves, a residual oil saturation value can be
generated for every single point on the production curve.
2.3 Fractured reservoir
Fluid flow in naturally fractured reservoirs is primarily through the high
permeability, low effective porosity fractures surrounding each matrix block. The
matrix blocks contain the majority of the reservoir pore volume and act as source or
21
sink to the fractures. The rate of recovery of oil and gas from a fractured reservoir is
function of size and properties of the matrix blocks, pressure and saturation history of
the fracture and the matrix system, and wettability (Thomas et al. 1983).
2.3.1 Dual porosity model
The dual porosity model can be used to handle naturally fractured reservoir
performance. In the dual porosity model, two sets of properties are specified: matrix
porosity and permeability, and fracture porosity and permeability. The main
difference between the dual permeability and the dual porosity model is that the fluid
can flow between matrix-matrix and fracture-fracture in dual permeability model,
while in the dual porosity model, flow does not occur between matrix-matrix.
The basic model of fluid flow in fractured media has been proposed by Barenblatt et
al. (1960) by applying the continuum approach. In this approach, a pair of average
properties is assigned to the fracture and matrix properties.
Warren and Root (1962) modeled a fractured reservoir with two parameters to
characterize a naturally fractured reservoir, with parameter (ω) relating fluid
capacitance of the secondary porosity and parameter (λ) relating the scale of
heterogeneity in the system. The model also assumes that interporosity flow occurs
under pseudo-steady state conditions.
Gilman and Kazemi (1982) developed a much more realistic model in which, variable
matrix block size was considered. Their dual porosity model was for two-phase flow,
22
in which gravity forces in the matrix/fracture transfer coefficients were included.
Their shape factor was calculated as
++=σ 2
z2y
2x L
1L1
L14 ,
where zyx L,L,L are the matrix block dimensions.
Thomas et al. (1981) developed a three dimensional, three-phase model for simulating
flow in naturally fractured reservoirs based on the matrix/fracture transfer function of
Warren and Root and accounts for gravity, capillary pressure, and viscous forces.
Both the fracture flow equations and matrix/fracture flow was solved implicitly for
pressure, water salutation, gas saturation, and saturation pressure.
2.3.2 Discrete fracture model
Natural fractures are known for their special subsurface flow and transport of
fluids. Discrete fracture network (DFN) techniques recently have gained increasing
attention in the oil industry (Dershowitz et al. 2000). The DFN is designed on
construction of fracture planes in 3D space using statistical properties of fracture
swarms, fractures geometry, and flow characteristics. The advantage of the discrete
fracture model over the dual porosity model is its ability to design complex fracture
patterns based on field data, such as cores, well logs, borehole images, seismic data,
and geomechanics. To reproduce the flow behavior in a fractured reservoir, the DFN
model can be conditioned by dynamic data such as well test, tracer and production
23
data. Such conditioning is important in fractured reservoirs because only a small
fraction of fractures in the DFN model might carry bulk of the fluid flow (Al-Harbi et
al. 2004).
Several investigators have published numerical models incorporating explicit discrete
fractures. Dershowitz et al. (2000) developed techniques to integrate the DFN and
dual porosity approach. These techniques allow analysts to maintain many of the
advantages of the dual porosity simulator approach without losing the realism of the
complex fracture system geometry and connectivity, as captured by the DFN model.
Sarda et al. (2002) developed a new DFN approach by using all transmissivity terms,
fracture/fracture, matrix/fracture, matrix/matrix, matrix/well and fracture/well in their
model. In this approach, matrix blocks of different volumes and shapes are associated
with each fracture cell depending on the local geometry of the surrounding fractures.
Basquet et al. (2004) developed a software to validate discrete fracture network. Their
DFN simulation approach was based on an optimized explicit representation for both
matrix and fracture media and a specific treatment for matrix/fracture and
matrix/matrix exchanges.
Quenes (2000) developed a new approach that combines the use of the continuum and
the discrete fracture modeling method. He introduced conditioned discrete fracture,
which was used to build a realistic and detailed model of flow in discrete fractures. In
addition, his new approach determines the number of fractures in each grid block,
based on the value of fracture intensity provided by continuum model.
24
2.4 Review of Cantarell Oil Field
The Cantarell field, which is the largest oil field in Mexico and sixth largest
oil field in the world, is located about 80 kilometers (km) offshore of the Yucatan
Peninsula in the Bay of Compeche, Mexico as shown in Fig. 2.1.
The Cantarell surface area is about 162 square kilometers (km2). It is composed of
four major fields: Akal, Nohoch, Chac and Kutz. The Akal field is the largest of the
complex with 91% of the original oil volume. The average depth for the Akal field is
estimated at 2300 meters (m) below sea level, and a pay zone thickness of about 1200
(m). It is a highly fractured carbonate reservoir with large volumes of vugs from
Jurassic, Cretaceous, and lower Paleocene geological ages (Rodriguez et. al 2001).
Two type of sedimentary accumulation have been documented near or at Cretaceous-
Tertiary boundary stratigraphy across the Golf of Mexico (Murillo et al. 2002).
The Cretaceous-Tertiary boundary stratigraphy was affected by diagenetic and
deformation history at the Cenozoic time which is more susceptible to dissolution,
dolomitization and fracturing processes that resulting in an extremely complicated,
naturally fractured and vuggy carbonate reservoirs. Pore types are very diverse and
include inherited porosity as well as vuggy, intercrystalline, and fracture porosity
(Murillo et al. 2002).
Hydrocarbon production from the field comes from two intervals of carbonate rocks.
The deepest is in the lower Cretaceous, represented by dolomitized and fractured
limestone. The upper is in the Paleocene-upper Cretaceous and is made of
25
dolomitized sedimentary breccia composed of subangular to subrounded mudstone
exoclasts and wackestone bioclasts deposited in a slope environment. The size of the
vugs varies from 1 to 15 millimeters (mm). In some areas, fracturing is intense and in
general, two fracturing systems are most important: horizontal fractures and vertical
fractures to stratification (Lopez and Gonzalez 2001).
There are three production zones within the Tithonian- Cretaceous Petroleum system:
Kimmeridgian, Cretaceous, and Eocene. The Cretaceous period formations have the
highest production rate in the Bay of Campeche. These source rocks range in
thickness from 35 to 310 meters and their source potential index (SPI) is up to 16
metric tons of hydrocarbons in immature source rocks in the northeastern part, and up
to 27 metric tons in the mature part of the system, in the south-central area. Data from
two field formation tests are shown in Table 2.1 and Table 2.2 (Lopez and Gonzalez
2001).
Typical total porosity in the reservoir is 7% and up to 25% of it may correspond to
secondary porosity (fractures, microfractures and vugs). Typical permeability in the
matrix and fracture media is 0.3 and 5000 md, respectively (Rodriguez et al. 2001).
Akal has produced under full gravity segregation condition and subject to natural
thermal convection. The gas-oil contact has been steadily moving through the years to
its current thickness of 730 (m). Water encroachment from an aquifer has also taken
place, and water-oil contact has moved 480 m from its original position of 3200 m
below sea level (Rodriguez et al. 2001).
26
There is a possibility that convection phenomena may be occurring in the Cantarell
oil field because convection is a complex phenomenon that occurs in thick and highly
fractured reservoirs and it results from a combination of thermal gradients, gas
liberation at gas-oil contact and gravity segregation, and it is made possible by high
vertical permeability. This statement has been confirmed by sampling oil at three
different zones of the reservoir. It observed that the deeper oil is lighter (Manceau et
al. 2000).
Natural depletion of the Akal reservoir has caused a pressure decline from its original
average value of 270 kg/cm2 to its current value of 105 kg/cm2. This has led to a
decreasing production rate (Rodriguez et al. 2001).
Initially, Cantarell produced from Akal field at an average rate of about 29,000
STB/D per well, but in 1995 its average production rate was about 7,000 STB/D per
well. When the Cantarell project was conceived, it required 150 gas-lift assisted wells.
Reservoir simulation studies indicated that pressure maintenance was required to
optimize hydrocarbon recovery in the Cantarell complex. Among the gas injection
technologies, nitrogen was selected by considering availability, cost, safety, handing
infrastructure, environmental and reservoir issues (Rodriguez et al. 2001).
Laboratory results and numerical studies demonstrated that a greater recovery of oil is
achieved in the gas cap than in the zone encroached by water. This is due to the
favorable structural reservoir conditions with a great vertical transmissibility, which
27
resulting a very efficient gravitational segregation in the gas cap, thereby giving up to
a 20 percent higher recovery than a water flood (Limon-Hernandez et al. 2001).
28
Table 1
Cantarell-3068 Formation Test I
Upper Cretaceous Breccia
Temperature at depth 3432-3600 m 124.9 C
Permeability 3,730 md
Static pressure at 3,432 md 311.3 kg/cm2
Flowing pressure at depth 3432-3600 m 298.2 kg/cm2
Pressure fall 13.1 kg/cm2
Damage factor +118
Qoil: tubing 4½” and f 2” (with damage) 8,582 bpd
Qgas: tubing 4½” and f 2” (with damage) 1.972 mmscf/d
Gas/oil relationship 41 m3/m3
Table 2.1: Cantarell formation test 1 Data (Lopez and Gonzalez 2001)
Table 2
Cantarell-3068 Formation Test II
Upper Jurassic
Temperature at 4,038 m 139 C
Permeability 3,730 md
Static pressure at 4,038 md 438.23 kg/cm2
Flowing pressure at 4,038 md 407 kg/cm2
Pressure fall 31.23 kg/cm2
Damage factor
Qoil: tubing 4½” and f ¾” (with damage) 8,182 bpd
Qgas: tubing 4½” and f ¾” (with damage) 4.1 mmscf/d
Gas/oil relationship 89.23 m3/m3
Table 2.2: Cantarell formation test 2 Data (Lopez and Gonzalez 2001)
29
Fig. 2.1: Location of Cantarell oil field (Limon-Hernandez et al. 2005)
30
CHAPTER 3: Use of Gas Tracers for Reservoir Characterization
The major difference between gas and aqueous-phase tracer tests is the selection of
the tracers to reflect the gas phase as displacing fluid.
3.1 Partitioning coefficient for gas tracers
The amount of tracer in each phase depends on its partition coefficient to each
phase. This requires that we first calculate the saturation of each phase and then
impose tracer concentration calculation for the phase.
Partitioning coefficient of tracer i, can be defined from a mass balance between the
gas and oil phase (Maroongroge 1994):
)Sρω+Sρω(φV=n ooo,iggg,iBi , (3.1)
where
in = total mass of tracer i,
=ω g,i mass fraction of tracer i in the gas phase,
=ω o,i mass fraction of tracer i in the oil phase.
Defining partition coefficient as
31
g,i
o,iTi ω
ω=K (3.2)
And substituting TiK in the above equation and solving for g,iω and o,iω yields
)SρωK+Sρω(φV=n oog,iTiggg,iBi (3.3)
)SρK+Sρ(φVn
=ωooTiggB
ig,i (3.4)
g,iTio,i ωK=ω (3.5)
We can use tracer concentration on mass per volume basis:
gg,ig,i ρω=C (3.6)
oo,io,i ρω=C (3.7)
g,i
o,iTi C
C=K (3.8)
where
=C g,i mass of tracer i per volume in the gas phase
=C o,i mass of tracer i per volume in the oil phase.
Note that TiK values from Equation (3.2) and Equation (3.3) are numerically
different by a factor equal to the oil-gas density ratio.
The partition coefficient for a gas tracer can be constant in the reservoir or as a
function of pressure.
32
3.2 Estimation of partition coefficient for gas tracers
The accuracy of the oil saturation estimation depends on the accuracy of the
estimation of tracer partitioning coefficients, at reservoir conditions.
Perfluorocarbon gas tracers (PFT’s) have been selected for this study. PFT’s are a
family of perfluorinated alkyl cycloalkanes. Table 3.1 shows the formulation and
properties of selected gas tracers. The detection limit of PFT’s is 1510− liter of PFT’s
per liter of reservoir gas (Senum et al., 1992).
Tracer partition coefficients can be accurately estimated based on vapor-liquid
equilibrium of tracers in reservoir fluid. The composition of the reservoir fluid used in
this study was obtained from PVT collected frm a typical oil field and it shown in
Table 3.2. The vapor-liquid equilibriums i
ii x
yK = , which obtained for reservoir
fluids components and tracers by flash calculation in PVT-SIM simulator at reservoir
conditions (reservoir temperature and pressure). The equilibrium ratio is then
converted to the partition coefficient (Maroongroge 1994).
Vi
L
Ti ξKξK = (3.9)
where
=TiK Partitioning coefficient
=ξL Liquid phase molar density (lb mole/ft3)
=ξV Vapor phase molar density (lb mole/ft3)
33
The equilibrium ratio and tracer partition coefficient are given in Table 3.3.
3.3 Simulation of tracer flow in slimtube
Dugstad et al. (1992) used a slimtube displacement experiment to test
conventional radioactive gas tracers and perflurocarbon gas tracers.
The objectives of simulating the slimtube displacement were to check the ECLIPSE
gas tracer option and comparing results with UTCOMP results that had been done in
good accuracy by Maroongroge (1994).
The slimetube experiment has been described in detail by Dugstad et al. (1992) and
Maroongroge (1994) and will be described briefly here. A thin and long tube of 5 mm
in diameter and 12 m in length was filled with oil wet Ottawa sand. The porosity of
the packed tube was 35%. The tube was saturated with liquid decane and displaced
with methane gas until residual oil saturation was reached.
The oil and gas saturation were calculated from the weight measured and the
estimated densities of both phases. Tracers were injected with injecting gas (methane)
at one end of the tube and produced from the other end. Produced tracers were
measured by liquid scintillation method for the radioactive tracers and gas
chromatography for the chemical tracers. The detection limit for the chemical tracer
was 1510− liter/liter. All tracers were injected in the same experiment so that the
partition coefficient of each tracer could be compared.
34
Gravity was considered negligible since the diameter of the tube was much smaller
than the length of the tube.
The retardation in the produced tracer concentration resulted from the different
partition coefficient of each tracer, so partition coefficients were calculated from the
retardation of each tracer. Oil was at residual saturation and gas was the only mobile
phase:
S
MRTi V
VVK −= (3.10)
where
=VM Volume of mobile gas
=VR Retention volume,
=VS Volume of stationary oil
Injection rate was assumed to be constant during the experiment, therefore the tracer
retention volume were calculated by multiplying the injection rate by the tracer
retention time.
RinjR TqV = (3.11)
The Tracer retention time was obtained from the peak arrival time of produced tracer
concentration. The volume of the residual oil and mobile gas were calculated from a
material balance. Retardation factor and partition coefficient have the following
relation:
35
or
ortiT S1
SK1R
−+= (2.23)
Location of each tracer peak concentration in the plot of tracer concentration versus
injected mobile phase volume ( MV ) determines the retardation factor of each tracer.
Maroongroge (1994) simulated the experiment with UTCOMP and obtained an
excellent match with the experiment. We tried to model the experiment using data
that Maroongroge used in his simulation, but faced problems with ECLIPSE.
Definition of partition coefficient in ECLIPSE is based on reservoir conditions that is
difficult to keep constant during the simulation since pressure and formation volume
factor are not constant in the reservoir at all times, and all places. Its units are also not
consistent since a partition coefficient value in ECLIPSE has to be multiplied by gas
formation volume factor and divided by oil formation volume factor:
gig
oioETi BC
BCK = (3.12)
ig
ioUTTi C
CK = (3.13)
o
g)ECLIPSE(T)UTCOMP(T B
BKK = (3.14)
gB = gas formation volume factor, MSCF
rb
oB =oil formation volume factor,STB
rb
36
The ECLIPSE manual does not clearly define the partition coefficient. Numerical
dispersion was another problem in ECLIPSE for this simple experiment We modeled
the slimtube by 3000x1x1 grid blocks and more than 2000 time steps for a 3-day
tracer injection to overcome the problem.
Table 3.4 shows retardation factor of each tracer and corresponding partitioning
coefficient from Equation (3.8). The input data for the simulation are given in Table
(3.5).
The result of ECLIPSE simulation and experimental results by Dugstad et al. (1992)
is shown in the Figure 3.1. It can be observed that numerical dispersion is still a
problem for obtaining a good match of the tracer concentration peaks. However, the
retention times in HCPV are close and this is most important since the oil saturation
can be calculated from retention time.
3.4 Simulation of gas tracers in fractured reservoir
The simulation study was initiated with a three-dimensional reservoir. Tracers
were injected with nitrogen into a gas cap and tracer concentrations were measured at
the producer. Oil saturations were calculated using the method of moments and the
comparison between the known model values and the estimated values were plotted.
The reservoir was considered a fractured reservoir, so first the dual porosity model
was used, and then later the discrete fracture model was used.
37
3.4.1 Reservoir parameters and geology data for base case simulation
Our simulations are based on the Cantarell oil field reservoir, which is the
largest oil field in Mexico. Data has been prepared from several Offshore Technology
Conference papers. The Cantarell oil field is located about 80 kilometers (km)
offshore of the Yucatan Peninsula in the Bay of Compeche.
The Cantarell surface area is about 162 square kilometers (km2). The average depth of
the Akal field is estimated at 2300 meters (m) below sea level, with a pay zone
thickness of about 1200 (m). It is a highly fractured carbonate reservoir with large
volumes of vugs from Jurassic, Cretaceous, and lower Paleocene geological ages
(Rodriguez et al. 2001).
Hydrocarbon production from the field comes from two intervals of carbonate rocks.
The deepest is in the lower Cretaceous, represented by dolomitized and fractured
limestone. The upper is in the Paleocene-upper Cretaceous and is made of
dolomitized sedimentary breccia composed of subangular to subrounded mudstone
exoclasts and wackestone bioclasts deposited in a slope environment. The size of
vugs varies from one to 15 millimeters (mm). In some intervals fracturing is intense
and in general two fracturing systems are most important, horizontal and vertical
fractures (Lopez et al. 2001).
Typical total porosity in the reservoir is 7% and up to 25% of it may correspond to
secondary porosity (fractures, microfractures and vugs). Typical absolute
38
permabilities in the primary and secondary media are 0.3 and 5000 md, respectively
(Rodriguez et al. 2001).
3.4.2 Base case Simulation with dual porosity model
The simulation domain is a quarter of a five-spot well pattern with dimensions
of 1000 ft long by 1000 ft wide by 1000 ft thick. Reservoir is divided in two regions:
a gas cap zone where the only mobile phase is gas and an oil zone where oil is the
mobile phase and water-oil contact is out of simulation domain, so in the initial case
there is no mobile water. The fracture and matrix permeabilities are 5000 and 0.2 md,
respectively. Residual oil saturation distribution has an exponential relation with
permeability distribution. So the residual saturations of oil and gas in rock matrix are
0.4 and 0.3, and in the fractures are 0.2 and 0.15, respectively. The matrix and
fracture porosity are 0.07 and 0.02, respectively. The shape factor is 0.36 assuming a
fracture spacing of 5 ft in the horizontal direction and 10 ft in the vertical direction.
Nitrogen injection was considered for pressure maintenance and a tracer slug with
one conservative tracer (K=0) and two partitioning tracers in a nitrogen injection with
partition coefficients of 1.5 and 2.5 based on UTCOMP definition was injected for
0.25 PV with nitrogen into the gas cap zone.
There is a rate constraint injector, which injects at constant rate of 5000 MSCF/D and
a pressure constraint producer, which produces under bottom hole pressure (BHP) of
950.0 psi. Capillary pressure is the only driving forces to produce oil from the matrix.
39
3.4.3 Results
Figure 3.2 shows the produced tracer concentration for three tracers with
different partition coefficients. The early arrival time of tracers and long production
tail in fractured reservoir can be observed. The early arrival time is for the
breakthrough of flowing traces in the fracture, and the long production tail is for the
diffusion of tracers into and out of the matrix since diffusion is a slow process.
Figure 3.3 shows oil production rate in dual porosity model; the first part with high
production rate indicates production from fracture and the low and long production
rate shows oil production from matrix. After about 2000 days of production, it can be
observed oil production rate is less than 10 STB/D. Figure 3.4 shows oil recovery in
dual porosity model. Most of the oil recovery comes from fractures because in this
case the fracture porosity and permeability are both large with respect to the matrix
porosity and permeability.
Oil saturation can be determined from two tracers of different partition coefficients
using method of moments as shown below.
3.5 Estimation of oil saturation and swept pore volume using method of
moments
Estimation of swept pore volume is very important in reservoir
characterization. It can be used to evaluate fluid flow pattern and maximize oil
40
recovery by infill drilling and designing an enhanced oil recovery process. The
reservoir swept pore volume between wells can be determined from first temporal
moment of concentration tracer production data of an interwell tracer test. Oil
saturation also can be estimated from first temporal moment of a partitioning
interwell tracer test (PITT).
3.5.1 Method of moments for dual porosity model
Method of moments theory for single porosity model was presented in Chapter
2. The derivation of method of moments has been presented in detail by Asakawa
(2005). Here we present a brief summary of his derivation for dual porosity model.
All of the assumptions and descriptions in Chapter 2 are valid for dual porosity model.
The mass conservation equation in dual porosity model is as follow:
For fracture:
0N.t
Cfmfi
fif =τ+∇+
∂∂
φr
(3.15)
where
∑==
pn
1jfijjfi CSC (3.16)
And for matrix:
0t
Cfm
mim =τ−
∂∂
φ (3.17)
where
41
∑==
pn
1jmijjmi CSC (3.18)
Adding matrix and fracture mass conservation equation:
0t
CN.
tC mi
mfifi
f =∂
∂φ+∇+
∂∂
φr
(3.19)
And total porosity is
mft φ+φ=φ (3.20)
Total tracer concentration is
t
mimfifti
CCC
φφ+φ
= (3.21)
Then mass conservation equation will be
0N.t
Cfi
tit =∇+
∂∂
φr
(3.22)
As it can be seen, Equation (3.22) is the same as Equation (2.1), so the first temporal
moment can be used in dual porosity model to calculate swept pore volume and oil
saturation in the reservoir.
The swept pore volume for three phases is
21
2112 )1()1(*))1(
1(KK
KVKVS
Vw
s −−−−
−= (2.18)
And the average oil saturation in swept pore volume is
)1()1(*)1(ˆ
2112
21−−−
−−=
KVKVVVSS wo , (2.17)
42
where mean residence volume is
2V
dtC
dttqCV slug
0ig
0it
i −
∫
∫=
∞
∞
(2.15)
3.5.2 Estimation of average oil saturation and swept pore volume in dual
porosity media
ECLIPSE was used to simulate tracer test in a quarter of a five-spot well
pattern with dimension of 1000 ft long by 1000 ft wide by 500 ft thick. The fracture
and matrix permeabilities are 5000 and 0.2 md, respectively. The shape factor of the
reservoir is 0.36. The uniform residual saturation of oil, gas and water into the system
are 0.3, 0.2 and 0.2, respectively. Water is at residual saturation in the reservoir and
tracers do not partition into the water. Reservoir was divided in two zones: gas cap
zone, where the gas is the only mobile phase, and oil zone, where oil is the mobile
phase.
Tracer transport between the fracture and matrix is by diffusion and capillary
imbibition process.
Gas is injected into gas cap and 3 gas tracers of partitioning coefficients of 0.0, 1.5
and 2.5 based on UTCOMP definition were selected to be injected for 0.25 PV.
Figures 3.5 and 3.6 show the concentrations of the tracers at the producer. Figure 3.7
shows the tracers recovery for 2000 days. It can be observed that about 95.0 % of the
43
conservative tracer and 60.0% of the partitioning tracer (K=1.5) has been recovered at
one pore volume injection. It verifies flow of the tracers to the matrix. Diffusion
phenomena, mobile oil into the matrix, and capillary pressure help tracer transport to
the matrix.
The amount of tracer that diffuses into the matrix takes a long time to be produced
because diffusion is a very slow process. The long tail tracer production shows this
phenomenon. Oil saturation can be estimated from method of moments and by using
total tracer concentration.
ooggit CfCfC += (3.23)
Average oil saturation from method of moments and reservoir simulation has been
compared in Fig. 3.8 and swept pore volume from method of moments is shown in
Fig. 3.9. The volume of oil saturation calculated from the tracer data converge to the
simulated value after about 1600 days.
3.5.3 Estimation of average oil saturation and swept pore volume in dual
porosity media for different residual oil saturation in matrix and fracture
Residual saturation distribution is a function of permeability, so in a fractured
reservoir in which the matrix and fracture have different permeabilities, residual
saturations are different. In this case, we have simulated the same case as Section
3.4.2 with different residual oil, gas and water saturations in the matrix and fracture.
44
For a fracture, residual oil, water and gas saturations are 0.15, 0.15 and 0.10,
respectively. For matrix, residual oil, water and gas saturations are 0.30, 0.30 and 0.2,
respectively. The other properties are the same as Section 3.5.2.
Figures 3.10 and 3.11 show the concentration of tracers at the producer. Conservative
tracer profiles for layer 3 after 50 days and 250 days is given in Figures 3.12 and
3.13, respectively. Figures 3.14 and 3.15 show conservative tracer profiles for layers
8 and 9 after 250 days, respectively. Note that tracer slug injection was for 150 days.
The average oil saturation from the method of moments and simulation are compared
in Figure 3.16 and swept pore volume from method of moments is shown in Figure
3.17. From Figure 3.16, it can be observed that method of moments can estimate oil
saturation with mobile oil and even for different saturations in matrix and fracture in
dual porosity media when using total tracer concentration. Figure 3.18 shows the
tracers recovery for 2000 days of tracer production.
3.6 Conclusion
Simulation of slimtube flow displacement by ECLIPSE shows lots of
numerical dispersion even for 3000 grid blocks. However, its peak concentration
arrival time is in fair agreement with Dugstad et al. (1992) experiment.
Tracer tests in fractured reservoirs show early arrival time, long production
tails and extreme dilution of the tracer, so the separation of tracer peaks can not be
45
used to calculate an accurate oil saturation. However, the method of moments can
accurately estimate the oil saturation since it takes to account the tracer tail.
A constant partition coefficient is one of the assumptions used in method of
moment, but in ECLIPSE, iK depends on oil and gas formation volume factors,
oB and Bg , which depend on pressure. However, in this study we made the oil and
gas formation volume factors constant in the simulation.
The method of moments gave accurate values of oil saturation in the fractured
reservoirs for both the residual oil saturation and mobile oil saturation (using total
concentration of tracers) where simulated with ECLIPSE in this way.
46
Tracer Tfp Tb Pc Tc Wt ω ρ L
°C °C psia °R molem lb/lb g/cc PMCP -45 48 330.8 811.9 300 0.458 1.72 PMCH -39 76 310.2 870 350 0.482 1.80
Table 3.1: Property of selected tracers (Maroongroge 1994)
Component Mole
fraction Pc Tc Vc ω MW psia R ft3/lb mole lb-mol/lbm
N2 0.2 492 227 1.44 0.04 28 C1 0.2987 667.4 343.1 1.5698 0.008 16.04
C2-C3 0.1675 669.18 598.92 2.5845 0.121 36.03 C4-C5 0.0929 519.38 795.12 4.7452 0.213 64.72 C6P1 0.1169 431 913 10.5654 0.296 86.18 C7P2 0.122 220 1420 32.3 0.59 323.08 PMCP 0.001 330.8 811.9 0.458 300 PMCH 0.001 310.2 870 0.482 350
Table 3.2: Fluid composition for estimating tracer partitioning coefficient
Symbol Name Chemical formula Equilibration ξ gas ξ liquid TiK
K Value lb mole/ft3 lb mole/ft3 PMCP methylcyclopentane C6F12 1.137 0.172 0.33 1.47
PMCH methycyclohexane C7F12 0.98 0.172 0.33 1.92 Table 3.3: Equilibrium ratio and partition coefficient of the selected tracers at reservoir condition
47
Tracer name Retention Volume Partitioning Coefficient TCH3 1.30 0.64
3314 CHCH − 1.91 1.93
PMCP 2.53 3.25 PMCH 3.69 5.72
Table 3.4: Partitioning coefficient and relative Retention volume for slimtube displacement
Dimensions (ft) Length Width Thickness
39.37
0.01453 0.01453
Porosity (fraction) 0.35 Rock compressibility (psi 1− ) Water compressibility (psi 1− ) Initial water saturation Tracer slug size (total pore volume) Initial oil saturation Initial gas saturation Reservoir temperature Initial reservoir pressure Injection rate of c1(methane) Number of Grid Blocks
0 0 0
0.006 0.32 0.68
122 °F (50 °C) 1450 psia
0.7 SCF/D
3000 x 1 x 1
Table 3.5: Data for simulation of slimtube displacement (Maroongoge 1994)
48
0.001
0.041
0.081
0.121
0.161
0.201
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Hydrocarbon Pore Volume injected
Nor
mal
ized
Tra
cer C
once
ntra
tion
simulated CH3T
Simulated 14CH3-CH3
Simulated PMCP
Simulated PMCH
Experiment CH3T
Experiment 14CH3-CH3
Experiment PMCP
Experiment PMCH
Fig 3.1: Comparison between produced tracer concentration history of Slimtube
Experiment with ECLIPSE simulation results.
0.0001
0.001
0.01
0.1
1
0 400 800 1200 1600 2000
Time, Days
Nor
mal
ized
trac
er c
once
ntra
tion
K=0.0
K=1.5
K=2.5
Fig 3.2 Normalized tracer concentration for dual porosity simulation case
49
0
2000
4000
6000
8000
10000
0 400 800 1200 1600 2000
Time, Days
Oil
Prod
uctio
n R
ate
STB
/D
Oil Rate STB/D
Fig 3.3 Oil production rate for dual porosity simulation case
0
0.1
0.2
0.3
0.4
0.5
0 400 800 1200 1600 2000
Time, Days
Oil
Rec
over
y E
ffici
ency
Oil Recovery %
Fig 3.4 Oil Recovery for dual porosity model simulation
50
0.001
0.01
0.1
1
0 400 800 1200 1600 2000Time, days
Nor
mal
ized
trac
er c
once
ntra
tion
K=0
K=1.5
Fig 3.5: Tracer concentration at the producer for dual porosity model (Semi-Log scale)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 400 800 1200 1600 2000Time, days
Nor
mal
ized
trac
er c
once
ntra
tion
K=0
K=1.5
Fig. 3.6: Tracer Concentration at the producer for dual porosity model
51
0
0.2
0.4
0.6
0.8
1
0 400 800 1200 1600 2000
time, Days
Trac
er re
cove
ry
K=0.0
K=1.5
K=2.5
Fig. 3.7: Tracers recovery for different partition coefficient in dual porosity media
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 400 800 1200 1600 2000
Time, days
Oil
Sat
urat
ion
Estimated Oil Saturation
Reservoir simulation oil saturation
Fig. 3.8: Oil saturation estimation from method of moments in dual porosity media with mobile oil
52
0
0.2
0.4
0.6
0.8
1
0 400 800 1200 1600 2000
Time, days
swep
t efic
ienc
y
Sweep Efficiency %
Fig. 3.9: Sweep efficiency estimation from method of moments in dual porosity media with mobile oil
0.001
0.01
0.1
1
0 400 800 1200 1600 2000Time, days
Nor
mal
ized
trac
er c
once
ntra
tion
K=0
K=1.5
Fig. 3.10: Tracer production concentration at the producer for different residual oil saturation in matrix and fracture (Semi-Log scale)
53
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 400 800 1200 1600 2000Time, days
Nor
mal
ized
trac
er c
once
ntra
tion
K=0
K=1.5
Fig. 3.11: Tracer production concentration at the producer for different residual oil saturation in matrix and fracture
Fig. 3.12: Conservative tracer concentration profile in layer 3 after 50 days of tracer injection.
54
Fig 3.13: Conservative tracer profile in layer 3 after 250 days
Fig. 3.14: Conservative tracer profile in layer 8 after 250 days
55
Fig. 3.15: Conservative tracer profile in layer 9 after 250 days
0
0.1
0.2
0.3
0.4
0.5
0.6
0 400 800 1200 1600 2000
Time, days
Oil
Sat
urat
ion
Estimated Oil Saturation
Reservoir simulation oil saturation
Fig. 3.16: Oil saturation estimation from method of moments in dual porosity media for different residual oil saturation in matrix and fracture
56
0
0.2
0.4
0.6
0.8
1
0 400 800 1200 1600 2000
Time, Days
swep
t efic
ienc
y
Sweep efficiency %
Fig. 3.17: Sweep efficiency estimation from method of moments in dual porosity media for different residual oil saturation in matrix and fracture
0
0.2
0.4
0.6
0.8
1
0 400 800 1200 1600 2000
Time, Days
Trac
er re
cove
ry
K=0.0K=1.5K=2.5
Fig 3.18: Tracers recovery for different partition coefficients in dual porosity media for different residual oil saturation in matrix and fracture
57
CHAPTER 4: Comparison of Discrete Fracture Model and Dual
Porosity Model for Gas Tracers
4.1 Driving forces in fractured reservoir
In fractured reservoirs, especially in the dual porosity model, the majority of
the oil is contained in the matrix, but the production of the oil to the wells is through
the high permeability fractures. Oil production from the matrix blocks needs at least
one driving force, otherwise the injected fluid can not sweep out the oil from the
matrix blocks.
Oil Expansion
As the pressure drops in the fracture system, oil will flow from the matrix to
equilibrate the matrix pressure with the surrounding fracture pressure. This oil
production is due to the oil expansion within the matrix, either above the bubble point
or by solution gas drive below the bubble point.
Capillary Imbibition
For a typical water wet system, matrix block has positive water-oil capillary
pressure and if water is injected into fractures, the water will flow under capillary
force to the matrix and oil will flow out.
58
Gravity Drainage/Imbibition
For a matrix block and surrounding fracture, the height difference between
two phases and density difference cause a pressure difference between the matrix and
fracture that allows oil flow to the fracture.
Viscous force
Viscous displacement of a fluid is simply the movement of that fluid when
pressure difference is applied. In fractured reservoirs, there is a pressure gradient in
the fracture system, which moves fluid through the fracture, toward production wells.
In most cases, this pressure gradient is small because fracture has high permeability in
which case it is reasonable to ignore the viscous displacement of the fluid from the
matrix by the fracture pressure gradient. However, if fracture permeability is
moderate, flow into and out of the matrix by the fracture pressure gradient would be a
significant driving force on production.
Diffusion
Oil may be produced by molecular diffusion between the matrix and fracture
during gravity drainage, in which the effect of diffusion mechanism on overall
recovery can be neglected on most systems. However for small matrix blocks,
diffusion can be a key mechanism in oil recovery.
59
4.2 Shape Factor study
Fracture/matrix fluid exchange process depends on shape factor and matrix
block size. The rate of fluid flow between matrix and fracture in dual porosity model
is significant and it depends on matrix-fracture transfer function which incorporates
with shape factor.
Fluid transfer between the matrix and fracture is defined as
)PP(k
tP
C mfmm
m −µ
σ=
∂∂
φ (4.1)
Where σ is the shape factor and is based on the size and shape of the matrix blocks.
The shape factor is defined as
mV)L
A(=σ , (4.2)
where A is the area of the matrix block contacted by fracture, L is the matrix block
size and Vm is the bulk volume of the matrix block.
Various shape factors reported in the literature:
Warren and Root obtained:
2L)2+N(N4
=σ (4.3)
For a cubic matrix block of dimension L and pseudo-steady state condition, N is the
number of the normal sets of fractures.
Kazemi et al. (1974) proposed:
60
]Lz
1Ly
1Lx
1[*4 222 ++=σ (4.4)
For fluid flow in three dimensions, the ECLIPSE simulator uses the above model for
shape factor definition.
Gilman and Kazemi extended the Kazemi (1974) shape factor to a more general form
for anisotropic, rectangular matrix blocks:
++=σ 2
z
z2y
y2x
xm
Lk
L
k
Lk4k (4.5)
IMEX simulator uses this model for shape factor definition.
Later Chang (1993) and Lim and Aziz (1995) recognized the time dependence of
shape factor. Edgar et al. (2003) developed time dependent shape factoras follows:
m
*D
D*s
tt
−
σ=σ For tD< *
Dt (4.6-1)
and
*s σ=σ For tD> *
Dt , (4.6-2)
where characteristic dimensionless time is approximately *Dt =0.1 and m is a function
of the flow rate and fracture aperture.
In general, shape factor is used as history matching parameter because it is impossible
to find fracture spacing for the entire reservoir.
61
4.3 Base case simulation for dual porosity and discrete fracture models
The purpose of this chapter is to compares dual porosity model and discrete
fracture model and discuss their advantages and disadvantages.
The base case simulation is a quarter of a five-spot pattern fractured reservoir. A
uniform residual oil saturation of 0.4 for matrix and 0.15 for fractures and a uniform
residual gas saturation of 0.3 for matrix and 0.10 for fractures was considered. The
reservoir has a porosity of 0.07 for matrix and a fracture porosity of 0.02. The
simulation field consists of a gas cap zone where gas is only mobile phase and oil
zone. Water-oil contact is not considered in the simulation domain and its residual
was neglected because it did not have any effect on gas tracer simulation. The
simulation field has dimensions of 100 ft in the X, Y and Z directions.
Complementary data for the simulation are given in Table 4.1.
Nitrogen injection has been chosen for pressure maintenance and a rate constraint
injector was considered to inject a conservative tracer and two partitioning tracers
with partitioning coefficients of 1.5 and 2.5 for 2.5% pore volume into the reservoir
and a pressure constraint producer was considered to produce oil, gas and tracers.
The simulation field modeled with the dual porosity, discrete fracture, and equivalent
single porosity.
62
4.4 Dual porosity Model
In a dual porosity model, the reservoir is divided in two systems; the rock
matrix, which usually provides the bulk of the reservoir fluid and the highly
permeable rock fractures, which usually provides fluid flow.
In the dual porosity model, matrix blocks are linked only through the fracture system,
and fluid flow through the reservoir takes place only in the fracture network with the
matrix blocks acting as sources.
Figure 4.1 shows an actual fracture reservoir and a modeled fractured reservoir with a
regular matrix and fracture, like dual porosity model.
4.4.1 Simulation of fractures by dual porosity model
To simulate a fractured reservoir by the dual porosity model, fracture porosity,
fracture permeability, and shape factor are essential reservoir parameters to define the
fracture properties.
Relative permeability and capillary pressure also play a significant role in fractured
reservoirs.
4.4.1.1 Relative permeability table in naturally fractured reservoir
In a fractured reservoir of gas-oil system, gas is the none-wetting phase and
oil is the wetting phase consequently moving a wetting phase from the matrix by the
none-wetting phase has small recovery efficiency.
63
A Corey-type model was used to model the relative permeability in this simulation.
Wettability has a significant effect on the end point relative permeability and relative
permeability exponent which are key factors in this model. The relative permeability
equation is
jenjrjrj )S(kk ο= (4.7)
For this study, there are only the gas and oil phases, so
g,oj,SS1
SSS
orgr
jrjnj =
−−
−= (4.8)
Two sets of relative permeability are considered for matrix and fracture based on their
residual saturation and end point relative permeability. Figure 4.2 and Fig. 4.3 show
relative permeability curves for the matrix and for the fracture, respectively.
4.4.1.2 Capillary pressure in naturally fractured reservoirs
Capillary pressure in fractured reservoirs is a significant factor for producing
oil from the matrix. Note that wettability has considerable effect on capillary pressure
phenomena and capillary pressure type.
The Corey-type capillary pressure model for gas-oil system is
pcjnnj
5.0pcjc )S()k/(CP φ= , (4.9)
where
64
oj,SS,)SS()SS(
S *o
or*
o*
nj =<−
−= (4.10)
gj,SS,)SS1(
)SS(S *
o*gr
*o
nj =>−−
−= (4.11)
Equation (4.10) is for the positive part of the capillary pressure and Equation
(4.11) is for the negative part of capillary pressure.
Based on Equation (4.9), capillary pressure depends on permeability, porosity, phase
saturation, and capillary exponent, therefore matrix and fracture should have different
capillary pressures.
In fractured reservoir simulations usually two sets of capillary pressure and relative
permeability tables are used for the fracture and the matrix.
The effect of capillary pressure has been studied for three cases: No capillary pressure
in the matrix and fracture, capillary pressure only in the matrix, and capillary pressure
in the matrix and fracture. Summarized data for Case 1 is given in Table 4.2. Figure
4.4 shows the oil saturation profile in the matrix for all three cases before gas
injection. Figure 4.5 shows the matrix oil saturation profile for Case 1 (no capillary
pressure) after 2000 days. It can be observed that oil production from the matrix is
less than 2%. Oil production rate and oil recovery of Case 1 is shown in Fig 4.6.
Summarized data for Case 2 (capillary pressure only in matrix) is given in Table 4.3
and Fig. 4.7 shows the capillary pressure curve for the first case. The system is oil-
wet and the capillary pressure is given with respect to the wetting phase. Figure 4.8
65
shows the oil recovery for this Case and Fig. 4.9 shows the oil saturation profile after
2000 days of gas injection, in which less than 3% oil production from the matrix can
be seen even for a large value of capillary pressure. This can be described by
wettability, because fractures are full of gas and the matrix contains oil and rock type
is oil-wet, so the oil does not like to be replaced by gas; in fact matrix capillary
pressure in this case help oil to remain in matrix.
In Case 3, there is capillary pressure in the fracture system. Summarized data is given
in Table 4.4 and relative permeability is same as before. Figure 4.10 shows the
capillary pressure curve for the matrix and fracture system. Figure 4.11 shows oil
recovery for this case and Fig. 4.12 shows the oil saturation profile after 2000 days of
gas injection, which illustrates considerable oil production from the matrix. It can be
described by fracture capillary pressure because fractures are full of gas and the rock
is oil-wet so fractures imbibe oil from the matrix. In the previous case, fracture did
not have capillary force to imbibe oil from the matrix.
4.4.2 Comparison of dual porosity model in IMEX and ECLIPSE
To analyze the behavior of the dual porosity model in ECLIPSE, we used
IMEX as a second simulator to compare results. The oil production rate for the dual
porosity model in IMEX and ECLIPSE are given in Fig. 4.13. There are significant
differences between ECLIPSE and IMEX. Oil recovery from the matrix in IMEX is
more than ECLIPSE. There are some differences in the recovery mechanism and the
66
shape factor definitions for ECLIPSE and IMEX. In this case, permeability
distribution is isotropic so both shape factors are the same. In ECLIPSE, driving
forces that mentioned in Section 4.1 has to be defined specifically in the simulation if
any of them is applied but in IMEX they are considered in the simulation
automatically.
4.4.3 Subgridding
In the dual porosity model, grid blocks can be divided into smaller grid blocks
to better characterize flow inside the matrix block and to model transient behavior of
the system. In ECLIPSE, matrix blocks can be divided as nested blocks in two
dimensions or as concentric blocks in three dimensions and it did not consider Z
direction subgridding, because in three dimension subgridding, all sub-divided grid
blocks have an identical center. Figures 4.14 and 4.15 show schematic view of
subgridding in ECLIPSE.
In IMEX there are two options for subgridding, horizontal subgrid which is as nested
grid block in the X-Y plane, and vertical subgrid which is as stack grid block in the Z
direction. Note that IMEX does not allow users to use both subgrid simultaneously.
The effect of subgridding on fluid flow and oil recovery for the dual porosity model
in ECLIPSE and IMEX is given in Fig. 4.16 through Fig. 4.19. For this simulation
case, changes are negligible but for some cases, subgridding affects oil recovery up to
50% .
67
4.5 Simulation of gas tracers by tracing an injection component in GEM
The GEM simulator does not have a tracer option for a tracer test. Tracers can
be modeled in this simulator by tracing a component of injection composition as a
tracer through the reservoir in a compositional simulator.
For this purpose, nitrogen is injected in two different ways, Nitrogen (A) as a
continuous injection for the purpose of pressure maintenance and Nitrogen (B) as slug
injection for the purpose of component tracing. Note that in both ways Nitrogen has
the same property and the only difference is the name. Nitrogen (B) is injected in 5%
of injection composition for 0.15 PV.
4.5.1 Simulation in dual porosity media
The simulation field is a quarter of five-spot well patterns in a fractured
reservoir. Uniform residual oil saturation for matrix is 0.4 and for fractures is 0.15.
the reservoir has a porosity of 0.07 for matrix and a fracture porosity of 0.02 and a
permeability of 5000 md and 0.2 md for fracture and matrix, respectively. The
simulation field consists of gas cap zone and oil zone. The fracture spacing is 5 ft in
the horizontal direction and 10 ft in the vertical direction. The simulation field is 1000
ft long, 1000 ft wide and 500 ft thick. In addition, gas cap thickness is 200 ft.
68
4.5.2 Comparison of the tracer test between ECLIPSE and CMG-GEM
The modeled tracer test in the compositional simulator GEM was compared
with black oil simulator ECLIPSE. Figure 4.20 shows the oil production rate for both
simulators and Fig. 4.21 shows the tracer response. It can be observed that the peak
arrival time for the two tracer tests approximately are in the same time. In addition, it
should be noted that fluid flow in the two simulators are different.
The purpose of this simulation was to compare the results of a gas tracer test in
ECLIPSE with another simulator to compare the tracer test for tracer transport in the
fracture and the matrix.
Tracer concentration profiles during gas injection for GEM is for the fracture and
matrix in Fig. 4.22 through Fig. 4.25 and for the ECLIPSE, it is given in Fig. 4.26 to
Fig. 4.29. It can be observed that the mole fraction profile of (N2B) in the matrix and
fracture are different by an order of about 30 times and the same thing is true for the
tracer profile in the matrix and fracture in the ECLIPSE simulator. Note that there is
no capillary pressure in both cases and the only mechanism for tracer transport is
diffusion, which is a slow process.
4.6 Simulation of fractures by modeling the fractures as discrete Fracture
network
The advantage of the discrete fracture model over the dual porosity model is
its ability to design complex fracture patterns based on field data, such as cores, well
69
logs, seismic data, and geomechanics. Discrete fracture is more realistic than dual
porosity, because in the dual porosity model, fractures are distributed uniformly
around the matrix while in the discrete fracture model it can be a heterogeneous
fracture distribution with heterogeneous permeability, porosity, and fracture spacing.
4.6.1 Problem to model fractures as discrete fracture
In the discrete fracture model, each fracture aperture has its own grid block, so
to calculate transmissibility between the matrix and fracture in the discrete fracture
model, large permeability contrast and large grid block size contrast between the
matrix and fracture pose problems.
To solve these problems, we increase fracture aperture size and reduce its porosity to
keep the fracture pore volume constant in the discrete fracture model.
4.6.2 Discrete fracture model
In this study, we use the discrete fracture model with the property of dual
porosity model to compare its performance with dual porosity. Each matrix block is
surrounded by fracture grid blocks. The fracture spacing is 10 ft in each direction,
which is the same as the dual porosity model. Fracture aperture in the discrete
fracture model is 1 ft. Total fracture porosity is 0.02, the same as the dual porosity
model and fracture porosity for each fracture grid block is calculated from total
fracture porosity and for this case, it is 0.08. Its permeability is 5000, the same as the
70
dual porosity model. Capillary pressure and relative permeability tables are the same
as the dual porosity model. Figure 4.30 through Fig. 4.33 show oil production rate,
recovery efficiency and tracer concentration comparisons between the dual porosity
and discrete fracture models. Figure 4.34 compares the oil production rate in
ECLIPSE and IMEX by discrete fracture model. The data for discrete fracture
simulation is given in Table 4.5
4.6.3 Grid refinement
Local grid refinement allows seeing what happens inside the grid blocks; it
allows users to refine a grid block in each direction to better characterize a grid block.
Grid refinement usually is used to refine grids near the well to better capture fluid
flow pattern near the wells. In discrete fracture model, matrix blocks can be refined to
better characterize fluid flow between matrix and fractures. Figure 4.35 shows a
schematic view of the grid refinement in discrete fracture model. A 2x2x2 refinement
was used for each matrix grid block to refine simulated discrete fracture model.
Figure 4.36 compares refinement and no-refinement models oil production rate. It can
be observed that there is no significant difference between original and grid
refinement case.
71
4.7 Simulation of fractures by modeling the fractures as equivalent single
porosity
When there is a big contrast between matrix and fracture permeability and
fractures occupy a large volume of the porous media, the reservoir could be modeled
as equivalent single porosity.
In this model the total porosity and permeability is fracture porosity and permeability.
It is assumed that production from matrix is small and negligible compare to fracture
production. Figures 4.37 and 4.38 show oil production rate and oil recovery
comparison between equivalent single porosity models, dual porosity model and
discrete fracture model. As expected most of oil production is from the fracture. The
difference between Equivalent single porosity model and the other models shows oil
recovery from the matrix.
4.8 Conclusion:
The rate of fluid flow between the matrix and fracture in the dual porosity
model is significant and it depends on matrix-fracture transfer function, which is
defined by the shape factor.
Capillary pressure depends on the permeability, porosity and wettability. End
point relative permeability strongly depends on wetting phase. For fracture system of
72
non-wetting phase displacing wetting phase the capillary pressure on the fracture
system is important to display wetting phase from the matrix.
The comparison between ECLIPSE and IMEX results for the dual porosity
model shows the difference in oil recovery from the matrix in simulators, which
results from the recovery mechanism definition in two simulators.
The discrete fracture model easily can handle all properties of the dual
porosity model and cover the certain assumptions, which make the dual porosity
model inaccurate for fluid flow in the matrix and fracture.
Transmissibity calculation is one of the problems in the discrete fracture
model and it is resulted from the big contrast between two neighbor grid blocks,
(matrix and fracture) size and permeability.
73
Dimensions (ft) Length 100 ft
Width 100 ft
Thickness 100 ft
No. of Grid Blocks 10 x 10 x 10 Grid Dimensions NX 10 NY 10 NZ 10 Matrix permeability 0.2 md Fracture permeability 5000 md Matrix porosity 0.07 Fracture porosity 0.02 Gas injection rate 10 MSCF/D Shape Factor 0.12 Fracture Spacing Length 10 ft Width 10 ft Thickness 10 ft Oil viscosity 2.5 cp Gas viscosity 0.0175cp Oil density 56.0 lb/ft3 Gas density 0.0615 lb/ft3 Sor in matrix 0.4 Sor in fracture 0.15
Table 4.1: Reservoir data for dual porosity model simulation Case Sgr Sor Kgr
o Koro Ng No Cpc Npc φ k
Matrix 0.3 0.4 1 0.2 2 2 0 0 0.002 0.07
Fracture 0.1 0.15 1 1 2 2 0 0 5 1
Table 4.2: Relative permeability and capillary pressure data for Case 1
74
Case Sgr Sor Kgro Kor
o Ng No Cpc Npc φ k Matrix 0.3 0.4 1 0.2 2 2 1 2 0.002 0.07 Fracture 0.1 0.15 1 1 2 2 0 0 5 1
Table 4.3: Relative permeability and capillary pressure data for Case 2
Case Sgr Sor Kgro Kor
o Ng No Cpc Npc φ k Matrix 0.3 0.4 1 0.2 2 2 1 2 0.002 0.07 Fracture 0.1 0.15 1 1 2 2 1 2 5 1
Table 4.4: Relative permeability and capillary pressure data for Case 3
Dimensions (ft) Length 109 ft
Width 109 ft
Thickness 109 ft
No. Grid Blocks 19 x 19 x 19 Grid Dimensions NX 10 NY 10 NZ 10 Matrix permeability 0.2 md Fracture permeability 5000 md Matrix porosity 0.07 Fracture porosity 0.02 Gas injection rate 10 MSCF/D Shape Factor 0.12 Fracture aperture 1 ft Fracture Spacing Length 10 ft Width 10 ft Thickness 10 ft Oil viscosity 2.5 cp Gas viscosity 0.0175cp Oil density 56.0 lb/ft3 Gas density 0.0615 lb/ft3 Sor in matrix 0.4 Sor in fracture 0.15
Table 4.5: Reservoir data for discrete fracture model simulation
75
Fig. 4.1 Typical fractured reservoir model.
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Gas saturation
Rel
ativ
e pe
rmea
bilit
y
KrgKro
Fig. 4.2: Relative permeability curve for matrix system contain gas and oil
76
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Gas saturation
Rel
ativ
e pe
rmea
bilit
y
KrgfKrof
Fig. 4.3: Relative permeability curve for fracture system contain gas-oil
Fig. 4.4: Matrix oil saturation profile before gas injection in simulation case
77
Fig. 4.5: Matrix oil saturation after 2000 days of gas injection for Case1
0
4
8
12
16
0 200 400 600 800 1000 1200
Time, Days
Oil
Rat
e ST
B/D
0
0.1
0.2
0.3
0.4O
il re
cove
ry e
ffic
ienc
y
Oil Rate
Recovery
Fig. 4.6: Oil production rate and oil recovery for case 1
78
0
4
8
12
16
20
0.3 0.4 0.5 0.6 0.7 0.8
Wetting phase saturation , So
Cap
illar
y pr
essu
re in
mat
rix
Pc-matrix
Fig. 4.7: Matrix capillary pressure for gas-oil system in case 2
0
4
8
12
16
0 200 400 600 800 1000 1200
Time, Days
Oil
Rat
e ST
B/D
0
0.1
0.2
0.3
0.4
Oil
reco
very
eff
icie
ncy
Oil Rate
Recovery
Fig.4.8: Oil production rate and Oil recovery efficiency for case 2
79
Fig 4.9: Matrix oil saturation after 2000 days gas injection for Case 2
0
5
10
15
20
0 0.2 0.4 0.6 0.8 1
Wetting phase saturation , So
Pc-m
atrix
0
0.125
0.25
0.375
0.5
Pc-F
ract
ure
Pc-matrixPc-fracture
Fig. 4.10: Matrix capillary pressure for gas-oil system in Case 3
80
0
4
8
12
16
0 200 400 600 800 1000 1200
Days
Oil
Rat
e S
TB/D
0
0.125
0.25
0.375
0.5
Oil
Rec
over
y ef
ficie
ncy
Oil Rate
Recovery
Fig. 4.11: Oil production rate and oil recovery efficiency for Case 3
Fig. 4.12: Matrix oil saturation after 2000 days of gas injection for Case 3
81
0
4
8
12
16
0 200 400 600 800
Time, Days
Oil
Rat
e S
TB/D
Eclipse
CMG-Imex
Fig. 4.13: Oil production rate in ECLIPSE and IMEX for dual porosity model
Fig. 4.14: Horizontal nested subgrided matrix block in ECLIPSE (ECLIPSE Manual
2004)
82
Fig. 4.15: Schematic view of concentric subgrided matrix blocks in ECLIPSE (Sinha
2004)
0
4
8
12
16
0 100 200 300 400 500
Time, Days
Oil
Rat
e ST
B/D
Dual porosity
SubgriddedModel
Fig. 4.16: Oil production rate for subgrided model and dual porosity model in ECLIPSE
83
0
0.125
0.25
0.375
0.5
0 100 200 300 400 500
Time, Days
Oil
Rec
over
y ef
ficie
ncy
Dual porosity model
Subgridded model
Fig. 4.17: Oil Recovery Efficiency for subgrided model and dual porosity model in ECLIPSE
0
4
8
12
16
0 100 200 300 400 500
Time, Dyas
oil R
ate
STB
/D
dual porosityModel
subgriddedModel
Fig. 4.18: Oil production rate for subgrided model and dual porosity model in IMEX
84
0
500
1000
1500
2000
2500
0 100 200 300 400 500
Time, Days
Oil
Rec
over
y Ef
ficie
ncy
Dual porosityModelSubgriddedModel
Fig. 4.19: Oil recovery efficiency for subgrided model and dual porosity model in ECLIPSE
0
1000
2000
3000
4000
5000
6000
0 100 200 300 400 500 600 700 800
Time, Days
Oil
prod
uctio
n ra
te,
STB
/D
Eclipse-Oil RateGem-Oil Rate
Fig. 4.20: Oil production rate comparison between ECLIPSE and GEM
85
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 100 200 300 400 500 600 700 800
Time, Days
Nor
mal
ized
trac
er C
once
ntra
tion
0
1.5
3
4.5
6
7.5
9
10.5
12
Mas
s (N
2B) R
ate,
LB
/Day
Conservative tracer
Mass (N2B) rate
Fig. 4.21: Comparison of tracer test in ECLIPSE and component tracing in GEM
Fig. 4.22: Mole fraction (N2B) in fracture after 50 days
86
Fig. 4.23: Mole fraction (N2B) in matrix after 50 days
Fig. 4.24: Mole fraction of (N2B) in fracture after 200 days
87
Fig. 4.25: Mole fraction of (N2B) in matrix after 200 days
Fig. 4.26: Tracer concentration profile in fracture after 50 days in ECLIPSE
88
Fig. 4.27: Tracer concentration profile in matrix after 50 days in ECLIPSE
Fig. 4.28: Tracer concentration profile in fracture after 200 days in ECLIPSE
89
Fig. 4.29: Tracer concentration profile in matrix after 200 days in ECLIPSE
0
4
8
12
16
0 200 400 600 800
Time, Days
Oil
Rat
e S
TB/D
Dual porosity Model
Discrete Fracture Model
Fig. 4.30: Oil Production rate in dual porosity model and discrete fracture model
90
0
0.125
0.25
0.375
0.5
0 100 200 300 400 500
Time, Days
Oil
Rec
over
y ef
ficie
ncy
Dual porosity model
Discrete fracture Model
Fig. 4.31: Oil recovery efficiency in dual porosity model and discrete fracture model
0
0.2
0.4
0.6
0.8
1
0 300 600 900 1200 1500
Time, Days
Nor
mal
ized
Tra
cer C
once
ntra
tion
Dual porosity model
Discrete fracture Model
Fig. 4.32: Conservative tracer response in dual porosity model and discrete fracture model.
91
0
0.2
0.4
0.6
0.8
1
0 300 600 900 1200 1500
Time, Days
Nor
mal
ized
Tra
cer C
once
ntra
tion
Dual porosity model
Discrete fracture Model
Fig. 4.33: Partitioning tracer response in dual porosity model and discrete fracture model.
0
4
8
12
16
0 200 400 600 800
Time, Days
Oil
Rat
e ST
B/D
Eclipse
CMG
Fig. 4.34: Oil production rate for discrete fracture model in ECLIPSE and IMEX
92
Fig. 4.35: Grid Refinement for discrete fracture model
0
4
8
12
16
0 200 400 600 800
Time, Days
Oil
Rat
e S
TB/D
Discrete Fracture Model
Discrete fracture modelrefinement
Fig. 4.36: Oil production rate for discrete fracture model and LGR
93
0
4
8
12
16
0 200 400 600 800 1000
Time, Days
Oil
Rat
e S
TB/D
Dual porosity modelDiscrete fracture modelEquivalent single porosity model
Fig. 4.37: Oil production rate comparison in dual porosity, discrete fracture and equivalent single porosity models
0
500
1000
1500
2000
0 200 400 600 800 1000
Time, Days
Oil
Rat
e S
TB/D
Dual porosity modelEquivalent single porosity modelDiscrete fracture model
Fig. 4.38: cumulative oil production rate in dual porosity model and equivalent single porosity model
94
CHAPTER 5: Application of Dimensionless Groups in Naturally
Fractured Reservoirs
5.1 Gravity Number Ng
Gravity number is the ratio of gravity force to viscous force, and it can vary
with injection rate, density difference, permeability, viscosity, length and thickness of
the reservoir. Ng is significant in determining the tendency of gravity override.
Lh
µugkρk
=N2
o2rx
g (5.1)
In fractured reservoir, by increasing gravity number, more fluid goes into the matrix
yielding more oil recovery. As shown by (Baker and Moore 1996) when Ng<0.1, the
flow regime is dominated by the viscous force, and when Ng> 10, the flow regime is
dominated by the gravity force. Therefore, there is a transition from viscous-
dominated flow to gravity-dominated flow when 0.1 <Ng<10. When a reservoir is
produced at low rate and there is a large density difference between displacing and
displaced fluids, gravity forces dominate over viscous forces; as the rate increase,
viscous force becomes stronger and cause the fluids to flow preferentially through
high permeability layers, then flow dominated by viscous force, this creates a vertical
non equilibrium situation. The gravity number gives an indication of the efficiency of
gravity forces in a displacement process.
95
Mobility ratio is another factor that the degree of gravity segregation depends on. In
fact, the effect of mobility ratio on gravity induces cross flow. At high mobility ratios,
the injected fluid has a greater tendency to by pass the oil and form a gravity tongue.
At a constant gravity number, mobility ratio provides gravity segregation of fluids
(Baker & Moore 1996).
5.1.1 Effect of Ng on oil recovery in dual porosity model:
Table 5.1 gives primary values of the parameters for the gravity number and
effective length to thickness ratio calculation in the following simulation with the
dual porosity model and the discrete fracture model. Figure 5.1 shows the effect of
gravity number on oil recovery efficiency and the summarized data for the figure is
given in Table 5.2.
As expected, with increasing gravity number, oil recovery efficiency increases. In
Case 1 viscous force dominated fluid flow through the reservoir because Ng<0.1, and
for Ng>1.0 at constant LR greater than 10.0 flow is dominated by gravity forces.
Note that Case 2 and Case 3 have large differences with respect to Case 1 that viscous
force drive fluid through reservoir.
5.1.2 Effect of gravity number (Ng) on oil recovery in discrete fracture model
The effect of gravity number on oil recovery in discrete fracture model is
shown in Fig. 5.2 and Table 5.3 gives the summarized data for Fig. 5.2.
96
In discrete fracture model with increasing gravity number, oil recovery will increase
and there is significant difference between Case 1 and Case 2 since flow is dominated
by gravity forces for Ng>1.0 and can be seen for case 2 and case 3 with increasing
gravity number oil recovery does not change significantly.
5.2 Effective length to thickness ratio:
LR is important to determine tendency of gravity override and cross flow
phenomena, because it controls the displacement to vertical equilibrium.
x
zL k
kHL
=R (5.2)
VE is a condition where the sum of all the driving forces in the direction
perpendicular to direction of bulk flow is zero and this condition happens by flow in
reservoir having large aspect ratio (Lake, 1989).
Based on numerical solution (Zapata, 1981) and analytical solution (Zapata and Lake,
1987) vertical equilibrium phenomena would happen for LR >10.
Actually, VE is a condition that causes maximum cross flow. LR depends on
reservoir length, reservoir thickness, horizontal and vertical permeability.
5.2.1 Effect of LR on oil recovery in dual porosity model
Effect of LR on oil recovery for dual porosity model is shown in Fig. 5.3 and
summarized data are given in Table 5.4.
97
The oil recovery efficiency will increase by increasing LR until it reaches vertical
equilibrium. As shown in Fig. 5.3 for dual porosity model vertical equilibrium occurs
at LR =40 because after that by increasing LR value to LR =80 the oil recovery
efficiency remains constant. Reservoir dimension has a significant effect on LR and
for large values of LR the reservoir behaves like a 1D reservoir. Real reservoirs have
a large length with respect to thickness.
5.2.2 Effect of LR on oil recovery in discrete fracture model
Figure 5.4 shows the effect of LR values on oil recovery in discrete fracture
model. As expected, recovery efficiency would increase by increasing effective
length to thickness ratio. Table 5.5 gives summarized data for Fig. 5.4.
Oil recovery efficiency will increase by increasing LR until it reaches vertical
equilibrium and for the discrete fracture model in gas-oil system, it happened at
LR =20 since for LR >20 oil recovery efficiency remain constant.
5.3 Dimensionless parameters for fractured reservoir tracer transport
In porous media, local equilibrium achieved for the tracer between solution
phase and carrying phases in most cases simply by controlling the flow rate of the
mobile carrying phase. In fracture media, however, low flow rate will increase matrix
diffusion effect (Deed 1999).
98
5.3.1 Mean residence time in fractured reservoir
The mean residence time is the ratio of first moment over zero moments.
Mean residence time for fractured reservoir is the sum of mean residence time of
tracer in fracture and matrix (Deeds 1999).
Mean residence time of conservative or partitioning tracer in fractured reservoir
calculated simply from theoretical mean residence time (Deeds 1999).
fRrateflowVolumetric
volumeFlowablet = (5.3)
fL
fg
Lgf R
ux
RubS2
xbS2t == (5.4)
fg
Lmm R
ubS2x)b2L(
tφ−
= , (5.5)
where retardation factor is
g
nnf S
SK1R += (5.6)
For the matrix, it is assumed there is no oil saturation in the matrix and for
conservative tracer fR =1 therefore the equation for the matrix mean residence time
can be written as
−
φφ
=
−
φ= 11
Sux1
b2L
Suxt
fg
mL
g
mLm (5.7)
The above equations can be expressed as dimensionless form by dividing tou
x L :
99
fDf Rt = (5.8)
−
φφ
= 11S
tfg
mDm (5.9)
−
φφ
+=+= 11S
Rtttfg
mfDmDfD (5.10)
5.3.2 Sensitivity analysis in dimensionless parameters of tracer transport
Retardation factor fR , Peclet number peN , Damkohler number DaN , matrix
number MaN , fracture porosity fφ andgf
mSφ
φ, are dimensionless parameters, which
may affect tracer transport. They are stated below:
g
nnf S
SK1R += (5.6)
L
Lpe D
uxN = (5.11)
u
xSK
KN L
NfN
awDa φ
= (5.12)
u
xLD4
N L2m
Ma = (5.13)
fφ
gf
mSφ
φ, (5.14)
100
where
L= fracture spacing
=mD Diffusion coefficient for the tracer in the matrix
=LD Dispersion coefficient
=φm Matrix porosity
fφ = Fracture porosity
=Lx Location of the effluent sampling point
u= Velocity
Matrix number MaN , fracture porosity fφ andgf
mSφ
φ, are special parameters for
fracture tracer transport (Deeds 1999).
5.3.2.1 Matrix number: MaN
MaN is the ratio of two characteristic time: the fracture mean residence time,
ux L , and the diffusion to the center of matrix characteristic time ,
m
2
D4L .
The parameter MaN accounts for the effect of matrix diffusion on the overall
transport. Table 5.6 shows the base case simulation data and Table 5.7 is the
summarized dimensionless parameter values for different MaN values. Figure 5.5
shows the effect of MaN on calculated mean residence time, for output tracer
101
response. Note that calculated mean residence time is given for conservative tracer,
fR =1 to eliminate effect of partitioning. When MaN =0.02 there is a very little
interaction between the tracer and matrix, therefore its mean residence time compared
to Equation (5.10) is actually fracture mean residence time.
For MaN =20.0 tracer reaches to equilibrium with the surrounding matrix, and its
mean residence time compare to Equation (5.10), which verifies our claim. For
MaN =0.8 there is some interaction between tracer and surrounding matrix but they
have not reached to equilibrium. Its mean residence time is between fracture mean
residence time and total mean residence time.
Figures 5.6 and 5.7 show tracer response curves in linear and semi-log scale. Note
that long tail of MaN =0.8 corresponds to its non-equilibrium condition.
5.4.2.2 Fracture porosity: fφ
The effect of fracture porosity on tracer response has been determined by
varying fracture porosity while keeping Sgf
mφφ constant. Table 5.8 shows
summarized parameter values for different fφ , Parameters have been calculated for
two sets of MaN values. Figures 5.8 and 5.9 show tracer response curves for
different fφ at constant MaN =0.02 and Figs. 5.10 and 5.11 shows tracer response
curves at MaN =20.0.
102
Different values of fφ have very little effect on tracer response curve while keeping
Sgf
mφφ constant since fφ is controlled by mφ in this condition.
5.4.2.3 Sensitivity analysis ofSgf
mφφ
This parameter consists of two characteristic parameters in fracture tracer
transport: First, the relative volume of matrix to fracture mφ / fφ , fφ specifies the
fraction of bulk volume occupied by fracture and mφ specifies fraction of the matrix
volume occupied by pore matrix volume, and 1/ gS parameter describe effect of
mobile fluid saturation on the tracer response.
Sensitivity of Sgf
mφφ can be analyzed in two sets of Matrix number:
Low Matrix number: MaN
At low matrix number MaN , equilibrium between matrix and fracture does not
occur. As we studied in the above section for very low matrix number like MaN =0.02,
there is very little interaction between tracer and matrix so its mean residence time
always will be around one fracture pore volume, regardless of the other parameter
values. Figure 5.12 shows an increase in Sgf
mφφ for MaN =0.02 has very little effect on
103
mean residence time even for large value ofSgf
mφφ . However, its trend describes that
an increase in Sgf
mφφ will result in an increase in mean residence time for the case that
there is a little interaction between the tracer and the matrix. Figures 5.13 and 5.14
show the tracer response for different Sgf
mφφ for MaN =0.02. The first three rows of
Table 5.9 summarize parameter values for this case.
High Matrix number: MaN
At high matrix number MaN =20.0, the flowing tracer into fracture is in
equilibrium with matrix, therefore decrease in fracture porosity increases the relative
volume of matrix to fracture so mean residence time (in terms of fracture volume)
would increase. This behavior satisfies Equation (5.10); based on Equation (5.10) an
increase in matrix volume or decrease in gas saturation increases the mean residence
time. Consequently, at high matrix number MaN , an increase in the parameter group
Sgf
mφφ will increase the mean residence time of the corresponding tracer. Figure 5.15
shows an increase in the mean residence time of the tracer for MaN =20.0 with
increasingSgf
mφφ . Figures 5.16 and 5.17 show tracer response curves for different
104
Sgf
mφφ for MaN =20. The linear decline at the end of each tracer response indicates
equilibrium for the tracer between fracture and matrix. The last three rows of Table
5.9 summarize the data parameters for this case.
5.5 Conclusion
In the discrete fracture model, vertical equilibrium for fractured reservoirs
occurred at RL>20 and in the dual porosity model this phenomena occurred at RL>40.
Ng is the ratio of the gravity force to the viscous force and in the discrete
fracture model and dual porosity model for Ng>1.0, flow through porous media is
dominated by gravity forces. The density difference is a significant factor in the
gravity override.
The matrix number strongly controls tracer transport in fractured reservoirs
between the matrix and the fracture. In addition, it is the ratio of the theoretical
fracture mean residence time to the diffusion time into the center of the matrix block.
For gas tracer tests, tracer transport between the matrix and the fracture reach to the
equilibrium condition at MaN =20.
High fracture porosity, low matrix porosity and low matrix number yield the
overall mean residence time approaches to the fracture mean residence time.
105
The accuracy of the oil saturation estimation in fractured reservoirs improves
if the overall mean residence time of the reservoir reaches to the sum of the matrix
and fracture mean residence times.
106
Kx= 0.2 md Kz= 0.2 md µ1 0.017 cp µ2 2.5 cp Ρo 56.65 lb/ft3 Ρg 0.0615 lb/ft3 g 9.8 m/s2
Krg 1 Kro 0.2 U 1.59E-07 ft/s Q 10000 SCF/D A 10000 ft2 H 100 ft L 100 ft
1 MSCF = 2.45 RB at 1500 psi Table 5.1: Primary parameters value for scaling group analysis
Table 5.2: Summarized data for Ng in dual porosity model
Case Lx h Ly Kz Kx u µ2 Kr2 RL Ng
Q MSCF/D
1 500 100 500 3.2 0.2 1.592E-07 0.5 0.2 20 0.02949 50 2 100 500 100 2000 0.2 1.592E-07 0.5 0.4 20 1.4747 50 3 100 100 100 8000 0.8 1.592E-07 0.5 1.0 20 14.747 50
Table 5.3: Summarized data for effect of Ng in discrete fracture model
Case Lx h Ly Kz Kx u µ2 Kr2 RL Ng
Q MSCF/D
1 500 100 500 3.2 0.2 1.596E-07 0.5 0.2 20 0.02949 50 2 100 500 100 2000 0.2 9.55E-08 0.5 0.5 20 3.07949 30 3 100 400 100 7000 1 1.99E-07 0.5 1.0 20 11.7949 50
107
Table 5.4: Summarized data for effect of LR in dual porosity model
Case Lx h Ly Kz Kx u µ2 Kr2 RL Ng Q MSF/D
1 500 100 500 0.008 0.2 1.592E-07 0.5 0.2 1 0.02949 50 2 500 100 500 0.2 0.2 1.592E-07 0.5 0.2 5 0.02949 50 3 500 100 500 0.8 0.2 1.592E-07 0.5 0.2 10 0.02949 50 4 500 100 500 3.2 0.2 1.592E-07 0.5 0.2 20 0.02949 50 5 500 100 500 12.8 0.2 1.592E-07 0.5 0.2 40 0.02949 50 6 500 100 500 51.2 0.2 1.592E-07 0.5 0.2 80 0.02949 50
Table 5.5: Summarized data for effect of LR in discrete fracture model
Table 5.6: Base case data for simulation of dimensionless parameter in fractured reservoir
Case Lx h Ly Kz Kx u µ2 Kr2 RL N
Q MSCF/D
1 500 100 500 0.008 0.2 1.596E-07 0.5 0.2 1 0.02949 50 2 500 100 500 0.2 0.2 1.596E-07 0.5 0.2 5 0.02949 50 3 500 100 500 0.8 0.2 1.596E-07 0.5 0.2 10 0.02949 50 4 500 100 500 3.2 0.2 1.596E-07 0.5 0.2 20 0.02949 50 5 500 100 500 12.8 0.2 3.186E-07 0.5 0.4 40 0.02949 100 6 500 100 500 51.2 0.2 3.186E-07 0.5 0.4 80 0.02949 100
Injection Rate 10 MSCF/D Reservoir Length 100 ft Reservoir Thickness 100 ft Reservoir Width 100 ft Velocity 0.013757 ft/s Diffusion Coefficient 0.000076 ft2/D Dispersion Coefficient 0.00005 ft2/D Fracture Spacing, L 10 ft
mφ 0.07
fφ 0.02 K1 0.0 K2 1.5 K3 2.5 Location of the effluent sampling point Lx 90 ft
108
MaN fφ Sgf
mφφ peN fR
0.02 0.02 5.83 41270 1.0 0.8 0.02 5.83 41270 1.0 20.0 0.02 5.83 41270 1.0
Table 5.7: Summarized parameters values for different MaN
MaN fφ Sgf
mφφ peN fR
0.02 0.002 5.83 41270 1.0 0.02 0.02 5.83 41270 1.0 0.02 0.2 5.83 41270 1.0 20.0 0.002 5.83 41270 1.0 20.0 0.02 5.83 41270 1.0 20.0 0.2 5.83 41270 1.0
Table 5.8: Summarized parameter values for case of different fφ
MaN fφ Sgf
mφφ peN fR
0.02 0.02 5.83 41270 1.0 0.02 0.02 29 41270 1.0 0.02 0.02 58.33 41270 1.0 20.0 0.02 5.83 41270 1.0 20.0 0.02 11 41270 1.0 20.0 0.02 29 41270 1.0
Table 5.9: Summarized parameter values for case of different Sgf
mφφ
109
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
time, Dyas
Rec
over
y ef
ficie
ncy
Ng=0.02949
Ng=3.0
Ng=11.80
Fig. 5.1: Effect of Ng on oil Recovery efficiency at LR =20 for dual porosity model
0
0.2
0.4
0.6
0.8
0 400 800 1200 1600 2000
Time, Dyas
Oil
Rec
over
y
Ng=0.02949
Ng=1.4747
Ng=14.747
Fig. 5.2: Effect of Ng on oil recovery efficiency at LR =10 for discrete fracture model
110
0
0.1
0.2
0.3
0.4
0 400 800 1200 1600 2000
Time, Dyas
Oil
Rec
over
y
R=1
Rl=5
Rl=10
RL=20
RL=40
R=80
Fig. 5.3: Effect of LR on oil recovery at constant Ng=0.02949 for dual porosity model
0
0.1
0.2
0.3
0.4
0.5
0.6
0 400 800 1200 1600 2000
Time, Days
Oil
Rec
over
y
RL=1
Rl=5
RL=10
RL=20
Rl=40
Rl=80
Fig. 5.4: Effect of LR on oil recovery efficiency at Ng=0.02949 and for discrete fracture model
111
0
1
2
3
4
5
6
7
0 5 10 15 20 25
Fracture pore volume (tDf )
Mea
n re
side
nce
time
(tDf ) Nma=0.002
Nma=0.8
Nma=20
Fig. 5.5: Effect of MaN on Mean residence time of tracer response
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Fracture pore volume (tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
Nma=0.002
Nma=0.8
Nma=20
Fig. 5.6: Effect of MaN on conservative tracer response
112
0.001
0.01
0.1
1
0 5 10 15 20 25
Fracture pore volume (tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
Nma=0.002
Nma=0.8
Nma=20
Fig. 5.7: Effect of MaN on conservative tracer response in Semi-Logscale
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Fracture pore volume ( tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
Fracture poro 0.002
fracture poro 0.02
fracture poro 0.2
Fig. 5.8: Effect of fφ on output tracer response at MaN =0.02
113
0.001
0.01
0.1
1
0 5 10 15 20 25
Fracture pore volume ( tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
Fracture poro 0.002
fracture poro 0.02
fracture poro 0.2
Fig. 5.9: Effect of fφ on output tracer response at MaN =0.02 (Semi-Log scale)
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25
Fracture pore volume tDf
Nor
mal
ized
trac
er c
once
ntra
tion
Fracture porosity 0.002
fracture porosity 0.02
fracture porosity 0.2
Fig. 5.10: Effect of fφ on output tracer response at MaN =20.0
114
0.001
0.01
0.1
1
0 5 10 15 20 25
Fracture pore volume tDf
Nor
mal
ized
trac
er c
once
ntra
tion Fracture porosity 0.002
fracture porosity 0.02
fracture porosity 0.2
Fig. 5.11: Effect of fφ on output tracer response for MaN =20.0 (Semi-Log scale)
0
0.2
0.4
0.6
0.8
1
1.2
0 5 10 15 20 25
Fracture pore volume ( tDf )
Mea
n R
ersi
denc
e Ti
me
( tD
f )
5.83
29
58.33
83.5S gf
m =φφ
33.58S gf
m =φφ
29S gf
m =φφ
Fig. 5.12: Effect of Sgf
mφφ on mean residence time for MaN =0.02
115
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20 25
Fracture pore volume (tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
5.83
29
58.33
29S gf
m =φφ
83.5S gf
m =φφ
33.58S gf
m =φφ
Fig. 5.13: Effect of Sgf
mφφ on tracer response curve for MaN =0.02
0.001
0.01
0.1
1
0 5 10 15 20 25
Fracture pore volume ( tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
5.83
29
58.33
29S gf
m =φφ
83.5S gf
m =φφ
33.58S gf
m =φφ
Fig. 5.14: Effect of Sgf
mφφ on tracer response curve for MaN =0.02 (Semi-Log scale)
116
0
4
8
12
16
0 5 10 15 20 25
Fracture pore volume inj
Nor
mal
ized
trac
er c
once
ntra
tion
5.83
11.0
29.0
11S gf
m =φ
φ
29S gf
m =φφ
83.5S gf
m =φφ
Fig. 5.15: Effect of Sgf
mφφ on mean residence time for MaN =20.0
0
0.04
0.08
0.12
0.16
0.2
0 5 10 15 20 25
Fracture pore volume ( tDf )
Nor
mal
ized
trac
er c
once
ntra
tion 5.83
11.0
29.0
29S gf
m =φφ
11S gf
m =φ
φ
83.5S gf
m =φφ
Fig. 5.16: Effect of Sgf
mφφ on tracer response curve at MaN =20.0
117
0.001
0.01
0.1
1
0 5 10 15 20 25
Fracture pore volume ( tDf )
Nor
mal
ized
trac
er c
once
ntra
tion
5.83
11.0
29.0
29S gf
m =φφ
11S gf
m =φ
φ
83.5S gf
m =φφ
Fig. 5.17: Effect of Sgf
mφφ on tracer response curve at MaN =20.0 (Semi-Log scale)
118
CHAPTER 6: Summary, Conclusions and Recommendations for
Future Work
The main objective of this research was to investigate gas tracer tests in naturally
fractured reservoirs and compare the dual porosity model and discrete fracture model
for gas tracer tests. The dual porosity model and discrete fracture model was
compared and the advantage of each model was studied.
The effect of dimensionless groups like gravity number and effective length to
thickness ratio in the dual porosity model and discrete fracture model was
investigated.
The method of moments was used to estimate average oil saturation in fractured
reservoirs for gas tracer tests. The results clearly demonstrate that the method of
moments is a simple, fast, and accurate way to estimate average oil saturation.
Sensitivity of dimensionless parameters for fracture tracer transports in the dual
porosity model was analyzed and the effect of fracture parameters in tracer transport
between the matrix and fracture was studied.
6.1 Use of gas tracers for reservoir characterization
The accuracy of oil saturation depends on the accuracy of partitioning
coefficient estimation. For gas tracers, partitioning coefficient was estimated by
119
equation of state. A gas tracer experiment was used to calibrate and test the accuracy
of gas tracer test in the ECLIPSE simulator. The same study had been performed
using the UTCOMP simulator, and the result was in good agreement with the
experiment. Results of the ECLIPSE compare to the UTCOMP had some deficiency
to simulate the same experiment.
The gas tracer test in fractured reservoirs was modeled with the dual porosity model
and the method of moments was used to estimate average oil saturation in dual
porosity media. The total tracer concentration was used to estimate average oil
saturation in mobile oil case. The results confirm that method of moments is a fast,
simple, and accurate way to estimate oil saturation; moreover, it does not need lots of
data from the reservoir under study.
6.2 Gas tracer test in naturally fractured reservoir model
The gas tracer test in naturally fracture reservoirs was modeled with the dual
porosity model and discrete fracture model. Fractured reservoirs are more
complicated to be modeled by the dual porosity model since dual porosity model has
some inaccurate assumption. The discrete fracture model has the characteristic of dual
porosity model and realistic properties of fractured reservoirs. A fractured reservoir
was simulated by the discrete fracture model with the property of dual porosity model
and the results was compared for two models. Several problems encountered while
modeling a fractured reservoir by the discrete fracture model. Large permeability
120
contrast, and large grid block size contrast, in two neighbor grid blocks pose
problems, in which affect transmissibility for fluid flow between the matrix and
fracture. Problems were eliminated by assuming large fracture aperture with low
porosity and high permeability.
Wettability in gas-oil system for fractured reservoirs affects the capillary pressure,
and the relative permeability. Property of capillary pressure in fractured reservoirs
and the effect of capillary pressure in oil recovery from the matrix in fractured
reservoirs were studied.
6.3 Dimensionless group study
Dimensionless groups are parameters, in which can give a sense of reservoir
properties for various reservoirs.
The effect of dimensionless groups in fractured reservoirs was studied by the dual
porosity and discrete fracture models. Gravity number and effective length to
thickness ratio was studied in the dual porosity model and the effect of each
parameter and their sensitivities were analyzed. The assumption of fluid flow through
porous media in the dual porosity model had some deficiency to manifests the effect
of LR perfectly since it is not sensitive to vertical/horizontal permeability ratio,
instead, the discrete fracture model can easily manifests the effect of various LR and
Ng.
121
6.4 Dimensionless group in fractured reservoir tracer transport
Tracer transport in fractured reservoirs was studied by using dimensionless
parameters. The tracer transport in fractured reservoirs is sensitive to some fracture
properties like, fracture porosity, matrix porosity, fracture spacing and some transport
properties like, diffusion coefficient, dispersion coefficient and velocity.
Properties were analyzed using some dimensionless parameters and sensitivity to
each parameter was analyzed. In gas tracer transport for Matrix number MaN > 20, the
fracture and matrix are in equilibrium condition.
6.5 Recommendations for future work
The discrete fracture model in this study was limited to a regular and a simple
fracture distribution around the matrix. It would be useful to study the complicated
fracture distributions and heterogeneous permeability, porosity, and fracture spacing
distributions in the discrete fracture model based on field data. In addition, discrete
fracture model can be modified to the assumption of the dual permeability model.
Simulations in this study were limited to a quarter of a five-spot well patterns. It
should be extended to indicate irregular well pattern.
The method of moments is a robust method for estimation of the average oil
saturation. It is recommended to use the inverse modeling to find the permeability and
the saturation distributions in naturally fractured reservoirs for gas tracer tests and
compare the results of both methods.
122
In the actual field tracer tests, tracers may have adsorption, decay ratio, dispersion
diffusion which we neglect some of their properties, in our simulations, for simplicity.
Further study should be carried out to investigate inclusion of the above, mentioned
factors in simulation studies.
123
Appendix A: Sample input files
A.1 ECLIPSE Input File for 3 phases flow of tracer test
=========================================================================== RUNSPEC =========Gas Injection in Fractured Reservoirs===================== =========================================================================== TITLE Gas Injection. DUAL POROSITY BLACKOIL 3D MODEL --------------------------------------------------------------------------- --DIMENSION: -- NX NY NZ DIMENS 10 10 20/ --The first half of the grid layers are matrix cells, the rest are fratures -- DUALPORO -- NSTACK 300 / --Phases OIL WATER GAS --Units FIELD DISPDIMS 2 4 4 / FMTOUT UNIFIN UNIFOUT -- --Dimension of the Equilibration Tables EQLDIMS 2 300 / --Full Implicit Solution FULLIMP -- TABDIMS 2 1 50 50 1 50 50 / --First #,The number of saturation tables entered using SGFN,etc.in PROPS --Second #,The number of PVT tables using PVTG,PVTO,etc in PROPS section. --Third #,The number of saturation nodes in any saturation table.
124
-- WELLDIMS -- max #well -- max # of connections per well -- 1 group, # wells in groups 100 100 1 100/ -- REGDIMS 3 3 / -- START 01 'jan' 2000 / -- --gravity drainage activated --GRAVDR --GRAVDRM --YES / --Request information required by GRAF for the run-time monitoring option MONITOR -- TRACERS -- oil water gas environ diffusion 0 0 3 0 'NODIFF' / PARTTRAC -- #.partition tracer #.K(p) #.pressure point 2 2 2/ =========================================================================== GRID =========================================================================== --- THE GEOMETRY OF THE SIMULATION GRID AND THE --- ROCK PERMEABILITIES AND POROSITIES ARE DEFINED. ---------------------------------------------------- -- THE CELL TOP DEPTHS -- ( TOPS ) ARE NEEDED ONLY IN THE TOP LAYER ( THOUGH THEY COULD BE. -- SET THROUGHOUT THE GRID -- Fracture Permeabilities are NOT multiplied by fracture porosity to yield -- a net fracture permeability. NODPPM DPGRID EQUALS 'DX ' 100 1 10 1 10 1 10/ MATRIX CELLS 'DY ' 100 1 10 1 10 1 10/ 'DZ ' 50 1 10 1 10 1 10/ 'PORO ' 0.07 1 10 1 10 1 10/ 'PERMX' 0.20 1 10 1 10 1 10/ 'PERMY' 0.20 1 10 1 10 1 10/ 'PERMZ' 0.20 1 10 1 10 1 10/ 'TOPS' 4000 1 10 1 10 1 1 / -- -------------------- FRACTURE PROPERTIES (PORE VOLUME) --Secondary Porosity=25% of Total Porosity (7%)=0.0175 --Includes Fractures, Microfractures and Vugs 'PORO ' 0.02 1 10 1 10 11 20 / FRACTURE CELLS 'PERMX' 5000.0 1 10 1 10 11 20 /
125
'PERMY' 5000.0 1 10 1 10 11 20 / 'PERMZ' 5000.0 1 10 1 10 11 20 / 'TOPS' 4000 1 10 1 10 11 11 / ---------------------------------------------- -- / SIGMA 0.36 / DZMTRX 10.00 / -- Create a initialization file w/ grid,props & region values INIT -- ============================================================================ PROPS ============================================================================ -- DEFINES THE REL. PERMEABILITIES, CAPILLARY -- PRESSURES, AND THE PVT PROPERTIES OF THE RESERVOIR FLUIDS ------------------------------------------------------------ -- KRW AND CAPILLARY PRESSURE ARE TABULATED AS -- A FUNCTION OF WATER SATURATION. STONE -- --Swat Krw Pcow SWFN 0.3000 0.0000 0.00 0.5000 0.00001 0.00 / -- For Fracture 0.15 0.0000 0.00 0.75 0.00001 0.00 / --Sgas Krg PCo-g SGFN -----------FOR MATRIX 0.20 0.0 0.0 0.225 0.025 0.03 0.250 0.06 0.46 0.275 0.11 1.25 0.30 0.18 2.35 0.35 0.35 3.47 0.40 0.56 5.45 0.450 0.78 8.40 0.500 0.95 16.63 / -- For Fracture 0.100 0.00 0.00 0.25 0.08 0.01 0.30 0.15 0.03 0.35 0.22 0.05 0.40 0.31 0.10
126
0.45 0.40 0.21 0.50 0.52 0.30 0.55 0.64 0.46 0.60 0.75 0.61 0.65 0.88 0.76 0.70 0.95 0.90 / --Soil Krow Krog SOF3 -----------FOR MATRIX 0.3000 0.000 0.000 0.3250 0.002 0.002 0.3500 0.014 0.014 0.3750 0.056 0.056 0.4000 0.080 0.080 0.4250 0.140 0.140 0.4500 0.190 0.190 0.4750 0.250 0.250 0.5000 0.300 0.300 / -- for fracture 0.1500 0.0000 0.0000 0.4000 0.3000 0.3000 0.7500 1.0000 1.0000 / -- PVT PROPERTIES OF WATER -- REF.PRESS Bw Compress. Visc Viscosidad PVTW 1500.0 1.029 3.13D-6 0.31 0 / -- --ROCK COMPRESSIBILITY ROCK 1532 4.5E-6 / MATRIX SYSTEM 1532 3.4E-5 / FRACTURE SYSTEM -- SURFACE DENSITIES OF RESERVOIR FLUIDS -- OIL WATER GAS DENSITY 56.65 62.4 0.06150 / TRACER 'TR1' 'GAS' '' / 'TR2' 'GAS' '' 'OIL' 1 / 'TR3' 'GAS' '' 'OIL' 1 / / TRACERKP 0.0001 0.7 10000 0.7 / 0.0001 1.15 10000 1.15 /
127
-- requests , flux limitting scheme to reduce numerical dispersion. TRACTVD / TRDIFTR1 7.7E-4/ TRDIFTR2 7.7E-4/ TRDIFTR3 7.7E-4/ DISPERSE 0 0.0 0.0000503 1.0 0.0000502 / 900 0.0 0.0000501 1.0 0.0000500 / / / -- PVT PROPERTIES OF DRY GAS (NO VAPOURISED OIL) -- PGAS FVFG VISCO PVDG 200.0 3.0947 0.0122 400.0 2.7715 0.0127 600.0 2.4591 0.0133 800.0 2.4589 0.0139 1000.0 2.4588 0.0145 1200.0 2.4587 0.0151 1400.0 2.4586 0.0156 1600.0 2.4585 0.0162 1800.0 2.4584 0.0168 2000.0 2.4583 0.0174 2145.0 2.3454 0.0178 2500.0 2.2476 0.0188 3000.0 2.19498 0.0203 3500.0 1.8093 0.0217 4000.0 0.7045 0.0232 5000.0 0.5589 0.0260 / -- POIL FVFO VISO Data for Undersaturated Oil PVDO 200.0 1.143 5.23 400.0 1.141 4.49 600.0 1.139 3.97 800.0 1.1372 3.58 1000.0 1.1371 3.32 1200.0 1.137 3.08 1400.0 1.1369 2.87 1600.0 1.1368 2.68 1800.0 1.1367 2.55 2000.0 1.1366 2.40 2145.0 1.1349 2.32 2500.0 1.1316 2.40 3000.0 1.1312 2.53 3500.0 1.108 2.64 4000.0 1.103 2.77
128
5000.0 1.093 3.00 / PMAX 5000 5000 / RPTPROPS DENSITY SWFN SGFN SOF3 TRACER / ============================================================================ REGIONS ============================================================================ FIPOWG SATNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1000*1 1000*2 / -- EQLNUM -- This keyword defines the Equilibration Region that belongs -- to every grid block. -- 2 fracture Region -- 1 matrix Region 1000*1 1000*2 / --Define tracer partitioning region. to use each K(p) for each tracer. TRKPFTR2 2000*1/ TRKPFTR3 2000*2/ =========================================================================== SOLUTION =========================================================================== --- DEFINES THE INITIAL STATE OF THE SOLUTION --- VARIABLES (PHASE PRESSURES, SATURATIONS AND GAS-OIL RATIOS) --------------------------------------------------------- -- -- DATUM DATUM OWC OWC GOC GOC RSVD RVVD SOLN -- DEPTH PRESS DEPTH PCOW DEPTH PCOG TABLE TABLE METH EQUIL -- -------FOR MATRIX 4000 1080 30000 0 4100 0 0 0 0 / -- -------FOR FRACTURE 4000 1080 30000 0 4100 0 0 0 0 / -- Ininitalaize tracer concentration for each grid block TBLKFTR1 2000*0.00 / TBLKFTR2
129
2000*0.00 / TBLKFTR3 2000*0.00 / -- OUTPUT CONTROLS (SWITCH ON OUTPUT OF INITIAL GRID BLOCK PRESSURES) RPTSOL POIL SGAS SOIL TBLK / RPTRST 'BASIC=3' -- keep all restarts, output every FREQth reporting period / ============================================================================ SUMMARY ============================================================================ RUNSUM EXCEL -- Requests that the run summary output, generated by the RUNSUM -- should be written in the FORMAT LOTUS 123. LOTUS FOPR FGPR ftpcTR1 ftpcTR2 FOPT FGOR FOSAT FOEWG ftpcTR3 ftptTR1 ftptTR2 ftptTR3 ftitTR2 FPR WBHP / FODEN FGDEN ============================================================================ SCHEDULE ============================================================================ -- The follow keyword with a series of mnemonics corresponds --to a solution or property vector to be written out to a file --which is readable by GRAF. RPTRST 'BASIC=1' 'TBLK' 'SGAS' 'TRACER' / RPTSCHED 'CPU' 'FIP' 'POIL' 'SOIL' 'SGAS' 'WELLS' SUMMARY=2' WELSPECS' 'TRACER' /
130
-- gas Re-Solution Rate DRSDT 0 / WELSPECS -- i j refdepth P1 G1 10 10 4100 'OIL' / I1 G1 1 1 4042 'GAS' / / COMPDAT --WELLS MUST BE COMPLETED IN THE FRACTURES -- i j k k Flag sat.tab ConnFactor Skin P1 10 10 20 20 OPEN 0 1* 0.5 / I1 1 1 12 12 OPEN 0 1* 0.5 / / -- Units (STB/day) WCONPROD P1 'OPEN' 'BHP' 8000 1* 4900 2* 950.01/ / -- Units (Mscf/day) WCONINJE I1 GAS OPEN RATE 5000 / / TUNING 0.001 5 0.05 0.15 3 0.3 0.1 1.25 0.75 / 0.1 0.001 1E-7 0.0001 10 0.01 1E-6 0.001 0.001 / 50 1 500 1 25 12 4*1E6 / TUNINGDP / NEXTSTEP / WTRACER -- Well Tracer Conc 'I1' 'TR1' 1.0 / 'I1' 'TR2' 1.0 / 'I1' 'TR3' 1.0 / / TSTEP 3*50 / WTRACER -- Well Tracer Conc 'I1' 'TR1' 0.0 / 'I1' 'TR2' 0.0 / 'I1' 'TR3' 0.0 / /
131
TSTEP 37*50 / END
132
A.2 ECLIPSE Input File for dual porosity model
======================================================================= RUNSPEC =========Gas Injection in Fractured Reservoirs================= ======================================================================= TITLE Gas Injection. DOUBLE POROSITY BLACKOIL 3D MODEL ----------------------------------------------------------------------- --DIMENSION: -- NX NY NZ DIMENS 10 10 20/ --The first half of the grid layers are matrix cells, the rest are fratures -- DUALPORO -- -- -- NSTACK 300 / --Phases OIL GAS --Units FIELD FMTOUT UNIFIN UNIFOUT -- --Dimension of the Equilibration Tables EQLDIMS 2 300 / --Full Implicit Solution FULLIMP -- TABDIMS 2 1 50 50 1 50 50 / --First #,The number of saturation tables entered using SGFN,etc.in PROPS --Second #,The number of PVT tables using PVTG,PVTO,etc in PROPS section. --Third #,The number of saturation nodes in any saturation table. -- WELLDIMS -- max #well -- max # of connections per well -- group, # wells in groups 100 100 1 100/ --
133
REGDIMS 3 3 / -- START 01 'jan' 2000 / -- --gravity drainage activated --GRAVDR --GRAVDRM --YES / --Request information required by GRAF for the run-time monitoring option MONITOR -- TRACERS -- oil water gas environ diffusion 0 0 3 0 'DIFF' / PARTTRAC -- #.partition tracer #.K(p) #.pressure point 3 3 3/ ========================================================================= GRID ========================================================================= --- THE GEOMETRY OF THE SIMULATION GRID AND THE --- ROCK PERMEABILITIES AND POROSITIES ARE DEFINED. ---------------------------------------------------- -- THE CELL TOP DEPTHS -- ( TOPS ) ARE NEEDED ONLY IN THE TOP LAYER ( THOUGH THEY COULD BE. -- SET THROUGHOUT THE GRID -- Fracture Permeabilities are NOT multiplied by fracture porosity to yield -- a net fracture permeability. NODPPM DPGRID EQUALS 'DX ' 10 1 10 1 10 1 10/ MATRIX CELLS 'DY ' 10 1 10 1 10 1 10/ 'DZ ' 10 1 10 1 10 1 10/ 'PORO ' 0.07 1 10 1 10 1 10/ 'PERMX' 0.20 1 10 1 10 1 10/ 'PERMY' 0.20 1 10 1 10 1 10/ 'PERMZ' 0.20 1 10 1 10 1 10/ 'TOPS' 4000 1 10 1 10 1 1 / -- -------------------- FRACTURE PROPERTIES (PORE VOLUME) --Secondary Porosity=25% of Total Porosity (7%)=0.0175 --Includes Fractures, Microfractures and Vugs 'PORO ' 0.02 1 10 1 10 11 20 / FRACTURE CELLS 'PERMX' 5000.0 1 10 1 10 11 20 / 'PERMY' 5000.0 1 10 1 10 11 20 / 'PERMZ' 5000.0 1 10 1 10 11 20 / 'TOPS' 4000 1 10 1 10 11 11 / ----------------------------------------------
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-- / SIGMA 0.12 / DZMTRX 10.00 / -- -- Create a initialization file w/ grid,props & region values INIT -- ======================================================================= PROPS ======================================================================= -- DEFINES THE REL. PERMEABILITIES, CAPILLARY -- PRESSURES, AND THE PVT PROPERTIES OF THE RESERVOIR FLUIDS ------------------------------------------------------------ -- KRW AND CAPILLARY PRESSURE ARE TABULATED AS -- A FUNCTION OF WATER SATURATION. --STONE -- --Sgas Krg Krog PCo-g SGOF -----------FOR MATRIX 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71/ --Sgas Krg Krog PCo-g -----------FOR Fracture 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25 0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40 0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89/ /
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-- PVT PROPERTIES OF WATER -- REF.PRESS Bw Compress. Visc Viscosidad --PVTW -- 1500.0 1.029 3.13D-6 0.31 0 / -- --ROCK COMPRESSIBILITY ROCK 1532 4.5E-6 / MATRIX SYSTEM 1532 3.4E-5 / FRACTURE SYSTEM -- SURFACE DENSITIES OF RESERVOIR FLUIDS -- OIL WATER GAS DENSITY 56.65 62.4 0.06150 / -- Pgas Bgas VISgas TRACER 'TR1' 'GAS' '' 'OIL' 1 / 'TR2' 'GAS' '' 'OIL' 1 / 'TR3' 'GAS' '' 'OIL' 1 / / TRACERKP 0.0001 0 10000 0/ 0.0001 0.7 10000 0.7 / 0.0001 1.15 10000 1.15 / -- requests , flux limitting scheme to reduce numerical dispersion. TRACTVD / -- PVT PROPERTIES OF DRY GAS (NO VAPOURISED OIL) -- PGAS FVFG VISCO PVDG 200.0 3.0947 0.0122 400.0 2.7715 0.0127 600.0 2.4591 0.0133 800.0 2.4589 0.0139 1000.0 2.4588 0.0145 1200.0 2.4587 0.0151 1400.0 2.4586 0.0156 1600.0 2.4585 0.0162 1800.0 2.4584 0.0168 2000.0 2.4583 0.0174 2145.0 2.3454 0.0178 2500.0 2.2476 0.0188 3000.0 2.19498 0.0203 3500.0 2.1093 0.0217 4000.0 1.97045 0.0232 5000.0 1.5589 0.0260 /
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-- -- POIL FVFO VISO /Data for Undersaturated Oil PVDO 200 1.143 1.046 400 1.141 0.898 600 1.139 0.794 800 1.1372 0.716 1000 1.1371 0.664 1200 1.137 0.616 1400 1.1369 0.574 1600 1.1368 0.536 1800 1.1367 0.51 2000 1.1366 0.48 2145 1.1349 0.464 2500 1.1316 0.48 3000 1.1312 0.506 3500 1.108 0.528 4000 1.103 0.554 5000 1.093 0.6 / / PMAX 5000 5000 / -- ACTIVATED FOR SOF3, SWFN, SGFN, PVTW, PVDG, DENSITY AND ROCK KEYWORDS RPTPROPS DENSITY SWFN SGFN SOF3 TRACER / -- =========================================================================== REGIONS =========================================================================== -- In order to quantify the oil in place in the Oil Zone FIPOWG SATNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1000*1 1000*2 / EQLNUM -- This keyword defines the Equilibration Region that belongs -- to every grid block. -- 2 fracture Region -- 1 matrix Region 1000*1 1000*2 / --Define tracer partitioning region. to use each K(p) for each tracer. TRKPFTR1 2000*1/ TRKPFTR2
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2000*2/ TRKPFTR3 2000*3/ ========================================================================= SOLUTION ========================================================================= --- DEFINES THE INITIAL STATE OF THE SOLUTION --- VARIABLES (PHASE PRESSURES, SATURATIONS AND GAS-OIL RATIOS) --------------------------------------------------------- -- -- DATUM DATUM OWC OWC GOC GOC RSVD RVVD SOLN -- DEPTH PRESS DEPTH PCOW DEPTH PCOG TABLE TABLE METH EQUIL -- -------FOR MATRIX 4000 1080 30000 0 4040 0 0 0 0 / -- -------FOR FRACTURE 4000 1080 30000 0 4040 0 0 0 0 / -- Ininitalaize tracer concentration for each grid block TBLKFTR1 2000*0.00 / TBLKFTR2 2000*0.00 / TBLKFTR3 2000*0.00 / -- OUTPUT CONTROLS (SWITCH ON OUTPUT OF INITIAL GRID BLOCK PRESSURES) RPTSOL POIL SGAS SOIL TBLK / RPTRST 'BASIC=3' -- keep all restarts, output every FREQth reporting period / ======================================================================== SUMMARY ======================================================================== RUNSUM EXCEL -- Requests that the run summary output, generated by the RUNSUM LOTUS FOPR FGPR ftpcTR1 ftpcTR2 FOPT FGOR
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FOEIG FOEWG ftpcTR3 ftptTR1 ftptTR2 ftptTR3 ftitTR2 / FPR WBHP / WOPR / WGPR / WTCTR1 / WTPCTR1 / WTPCTR2 / WTPTTR2 / WTPCTR3 / FODEN FGDEN --BFLLOO --BFLOG --BTCNFTR1 --BTCNFTR2 --BTCNSTR2 ======================================================================== SCHEDULE ======================================================================== RPTRST 'BASIC=1' 'TBLK' 'SGAS' 'TRACER' / -- RPTSCHED 'CPU' 'FIP' 'POIL' 'SOIL' 'SGAS' 'WELLS' SUMMARY=2' WELSPECS' 'TRACER' / -- -- gas Re-Solution Rate DRSDT 0 / WELSPECS -- i j refdepth P1 G1 10 10 4100 'OIL' / I1 G1 1 1 4042 'GAS' / / -- COMPDAT
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--WELLS MUST BE COMPLETED IN THE FRACTURES -- i j k k Flag sat.tab ConnFactor Skin P1 10 10 20 20 OPEN 0 1* 0.5 / I1 1 1 13 14 OPEN 0 1* 0.5 / / -- Units (STB/day) WCONPROD P1 'OPEN' 'BHP' 15 1* 9.90 2* 950.01/ / -- Units (Mscf/day) WCONINJE I1 GAS OPEN RATE 10 / / TUNING 0.001 5 0.05 0.15 3 0.3 0.1 1.25 0.75 / 0.1 0.001 1E-7 0.0001 10 0.01 1E-6 0.001 0.001 / 50 1 500 1 25 12 4*1E6 / TUNINGDP / NEXTSTEP / WTRACER -- Well Tracer Conc 'I1' 'TR1' 1.0 / 'I1' 'TR2' 1.0 / 'I1' 'TR3' 1.0 / / TSTEP 3*50 / WTRACER -- Well Tracer Conc 'I1' 'TR1' 0.0 / 'I1' 'TR2' 0.0 / 'I1' 'TR3' 0.0 / / TSTEP 37*50 / END
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A.3 ECLIPSE Input File for Discrete fracture model
================================================================= RUNSPEC =========Gas Injection in Fractured Reservoirs=========== ================================================================= TITLE Gas Injection. DOUBLE POROSITY BLACKOIL 3D MODEL -------------------------------------------------------------- -------------------------------------------------------------- --DIMENSION: -- NX NY NZ DIMENS 19 19 19/ NSTACK 250 / --Phases OIL GAS --Units FIELD FMTIN FMTOUT UNIFIN UNIFOUT --Dimension of the Equilibration Tables EQLDIMS --#Reg,#nodes in any press table 2 300 / --Full Implicit Solution FULLIMP TABDIMS 2 1 50 50 1 50 50 / --First#,The number of saturation tables entered using SGFN,etc.in PROPS --Second#,The number of PVT tables using PVTG,PVTO,etc in PROPS section. --Third#,The number of saturation nodes in any saturation table. -- WELLDIMS -- max #well -- max # of connections per well -- group, # wells in groups 100 100 1 100/ -- REGDIMS 3 3 / /
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START 01 'JAN' 2000 / --Request information required by GRAF for the run-time monitoring option MONITOR MEMORY / TRACERS -- oil water gas environ diffusion 0 0 3 0 'DIFF' / PARTTRAC -- #.partition tracer #.K(p) #.pressure point 3 3 3/ =================================================================== GRID =================================================================== -- Fracture Permeabilities are NOT multiplied by fracture porosity to yield -- a net fracture permeability. NODPPM / OLDTRAN / DX 6859*10 / DY 6859*10 / DZ 6859*10 / TOPS 361*4000/ PORO 6859*0.07/ permx 6859*0.2/ COPY PERMX PERMY / PERMX PERMZ / / EQUALS DY 1 1 19 2 2 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 4 4 1 19 / permx 5000 /
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permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 6 6 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 8 8 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 10 10 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 12 12 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 14 14 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 16 16 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / DY 1 1 19 18 18 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 2 2 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 4 4 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 6 6 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 /
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dz 1 1 19 1 19 8 8 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 10 10 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 12 12 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 14 14 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 16 16 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dz 1 1 19 1 19 18 18 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 2 2 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 4 4 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 6 6 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 8 8 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 10 10 1 19 1 19 / permx 5000 / permy 5000 /
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permz 5000 / poro 0.08 / dx 1 12 12 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 14 14 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 16 16 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / dx 1 18 18 1 19 1 19 / permx 5000 / permy 5000 / permz 5000 / poro 0.08 / / -- Create a initialization file w/ grid,props & region values INIT -- =================================================================== PROPS =================================================================== -- DEFINES THE REL. PERMEABILITIES, CAPILLARY -- PRESSURES, AND THE PVT PROPERTIES OF THE RESERVOIR FLUIDS SGOF -----------FOR MATRIX 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71/ --Sgas Krg Krog PCo-g -----------FOR Fracture 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25 0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40
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0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89/ / FILLEPS / / -- PVT PROPERTIES OF WATER -- REF.PRESS Bw Compress. Visc Viscosidad --PVTW -- 1500.0 1.029 3.13D-6 0.31 0 / --ROCK COMPRESSIBILITY ROCK 1532 4.5E-6 / MATRIX SYSTEM 1532 3.4E-5 / FRACTURE SYSTEM -- SURFACE DENSITIES OF RESERVOIR FLUIDS -- OIL WATER GAS DENSITY 56.65 62.4 0.06150 / -- Pgas Bgas VISgas TRACER 'TR1' 'GAS' '' 'OIL' 1 / 'TR2' 'GAS' '' 'OIL' 1 / 'TR3' 'GAS' '' 'OIL' 1 / / TRACERKP 0.0001 0 10000 0/ 0.0001 0.7 10000 0.7 / 0.0001 1.15 10000 1.15 / -- requests , flux limitting scheme to reduce numerical dispersion. TRACTVD / -- PVT PROPERTIES OF DRY GAS (NO VAPOURISED OIL) -- PGAS FVFG VISCO PVDG 200.0 3.0947 0.0122 400.0 2.7715 0.0127 600.0 2.4591 0.0133 800.0 2.4589 0.0139 1000.0 2.4588 0.0145 1200.0 2.4587 0.0151
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1400.0 2.4586 0.0156 1600.0 2.4585 0.0162 1800.0 2.4584 0.0168 2000.0 2.4583 0.0174 2145.0 2.454 0.0178 2500.0 2.4476 0.0188 3000.0 1.9498 0.0203 3500.0 1.8093 0.0217 4000.0 1.7045 0.0232 5000.0 1.5589 0.0260 / -- -- POIL FVFO VISO /Data for Undersaturated Oil PVDO 200 1.143 1.046 400 1.141 0.898 600 1.139 0.794 800 1.1372 0.716 1000 1.1371 0.664 1200 1.137 0.616 1400 1.1369 0.574 1600 1.1368 0.536 1800 1.1367 0.51 2000 1.1366 0.48 2145 1.1349 0.464 2500 1.1316 0.48 3000 1.1312 0.506 3500 1.108 0.528 4000 1.103 0.554 5000 1.093 0.6 / / PMAX 5000 5000 / -- ACTIVATED FOR SOF3, SWFN, SGFN, PVTW, PVDG, DENSITY AND ROCK KEYWORDS RPTPROPS DENSITY SWFN SGFN SOF3 TRACER / ==================================================================== REGIONS ==================================================================== -- In order to quantify the oil in place in the Oil Zone FIPOWG SATNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 / EQLNUM -- SPECIFY THE SATURATION FUNCTION REGION TO WHICH IT BELONGS 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 / --Define tracer partitioning region. to use each K(p) for each tracer. TRKPFTR1 6859*1/ TRKPFTR2 6859*2/ TRKPFTR3 6859*3/ =================================================================== SOLUTION =================================================================== --- DEFINES THE INITIAL STATE OF THE SOLUTION --- VARIABLES (PHASE PRESSURES, SATURATIONS AND GAS-OIL RATIOS) --------------------------------------------------------- -- DATUM DATUM OWC OWC GOC GOC RSVD RVVD SOLN -- DEPTH PRESS DEPTH PCOW DEPTH PCOG TABLE TABLE METH EQUIL -- -------FOR MATRIX 4000 1080 30000 0 4043 0 0 0 0 / -------FOR FRACTURE 4000 1080 30000 0 4043 0 0 0 0 / -- Ininitalaize tracer concentration for each grid block TBLKFTR1 6859*0.00 /
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TBLKFTR2 6859*0.00 / TBLKFTR3 6859*0.00 / -- OUTPUT CONTROLS (SWITCH ON OUTPUT OF INITIAL GRID BLOCK PRESSURES) RPTSOL POIL SGAS SOIL DENO TBLK / RPTRST 'BASIC=1' -- keep all restarts, output every FREQth reporting period -- 'FREQ=20' / -- =================================================================== SUMMARY =================================================================== RUNSUM EXCEL -- Requests that the run summary output, generated by the RUNSUM LOTUS FOPR FGPR ftpcTR1 ftpcTR2 FOPT FGOR FOEIG FOEWG ftpcTR3 ftptTR1 ftptTR2 ftptTR3 ftitTR2 FPR WBHP / WOPR / WGPR / WTCTR1 / WTPCTR1 / WTPCTR2 / WTPTTR2 / WTPCTR3 / FODEN FGDEN
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=================================================================== SCHEDULE =================================================================== RPTRST 'BASIC=1' 'TBLK' 'SGAS' 'TRACER' / -- RPTSCHED 'CPU=1' 'FIP' 'POIL' 'SOIL' 'SGAS' 'WELLS' SUMMARY=2' WELSPECS' 'TRACER' / -- -- gas Re-Solution Rate DRSDT 0 / / WELSPECS P1 G1 19 19 4100 GAS / I1 G1 1 1 4044 OIL / / -- COMPDAT P1 19 19 18 19 OPEN 0 1* 0.5/ I1 1 1 6 7 OPEN 0 1* 0.5 / / -- Units (STB/day) WCONPROD P1 'OPEN' 'BHP' 15 1* 9.70 2* 950.01/ / -- Units (Mscf/day) WCONINJE I1 GAS OPEN RATE 10 / / TUNING 0.05 5 0.1 0.15 3 0.3 0.1 1.25 0.75 / 0.1 0.001 1E-7 0.0001 10 0.01 1E-6 0.001 0.001 / 35 1 250 1 25 12 4*1E6 / TUNINGDP / NEXTSTEP / WTRACER -- Well Tracer Conc 'I1' 'TR1' 1.0 / 'I1' 'TR2' 1.0 / 'I1' 'TR3' 1.0 /
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/ TSTEP 3*50 / WTRACER -- Well Tracer Conc 'I1' 'TR1' 0.0 / 'I1' 'TR2' 0.0 / 'I1' 'TR3' 0.0 / / TSTEP 37*50/ END
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A.4 CMG-IMEX Input File for dual porosity model
**--------------------------------------------------------------------** ** GMcan001.DAT: Dual Porosity Model ** **--------------------------------------------------------------------** **--------------------------------------------------------------------** ** ** ** FILE: GMcant001.DAT ** ** ** ** MODEL: Fracture Gas Tracer Test ** ** DUAL POROSITY ** ** FIELD UNITS 3 COMPONENT FLUID ** ** ** **--------------------------------------------------------------------** ** ** ** ** **--------------------------------------------------------------------** ** CONTACT CMG at (403)531-1300 or [email protected] ** **--------------------------------------------------------------------** ************************************************************************ ** I/O Control Section ************************************************************************ *RESULTS *SIMULATOR *IMEX *TITLE1 ' GMcant001.DAT ' *TITLE2 ' Dual porosity ' *TITLE3 ' FRACTURED RESERVOIR' *INUNIT *FIELD *WPRN *WELL 1 **write well result everey 10 time changes *WPRN *GRID 1 *WRST *TIME **write restart file **DIM *MDIMPL 100 **DIM *MDICLU 200000 *OUTPRN *WELL *ALL *OUTPRN *RES *ALL **OUTPRN *TABLES *NONE *OUTPRN *GRID *SO SG PRES *WSRF *WELL *TIME **how frequency written to simulation result *WSRF *GRID *TIME **DIARY *CHANGES **IDENTIFY WHAT INFORMATION IS WRITTEN TO THE RESULT FILE *OUTSRF *WELL *OUTSRF *GRID *SG SO PRES
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*OUTSRF *RES *ALL ********************************************************************* ** Reservoir Description Section ********************************************************************* *GRID *cart 10 10 10 *KDIR *DOWN *DI *CON 10.0 *DJ *CON 10.0 *DK *CON 10.0 *DUALPOR **SUBDOMAIN **MINC 4 *SHAPE *GK *TRANSFER 3 **type of matrix-fracture model treat to phsaes *DIFRAC *CON 10 *DJFRAC *CON 10 *DKFRAC *CON 10 *DEPTH 1 1 1 4000.00 ** Depth to center of first block, in bottom layer. *POR *FRACTURE *CON 0.02 *POR *MATRIX *CON 0.070 *CPOR *FRACTURE 3.4E-5 *PRPOR *FRACTURE 1532 *CPOR *MATRIX 4.5E-6 *PRPOR *MATRIX 1532 *PERMI *FRACTURE *CON 5000 *PERMJ *FRACTURE *CON 5000 *PERMK *FRACTURE *CON 5000 *PERMI *MATRIX *CON 0.2 *PERMJ *MATRIX *CON 0.2 *PERMK *MATRIX *CON 0.2 ************************************************************************ ** FLUID PROPERTIES ************************************************************************ *MODEL *BLACKOIL *PVT *BG ** p rs bo Bg viso visg 500 100.000 1.137 0.002458 3.30 0.0145
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2500 300.01 1.338 0.00145 2.40 0.0188 8000.0 1000.1 1.400 0.00043 2.00 0.0400 *DENSITY *OIL 52.6 *DENSITY *GAS 0.0615 *DENSITY *WATER 62.4 *CO 0.000E *CVO 0.0 *BWI 1.029 *CW 3.31E-6 *REFPW 1500 *VWI 0.5 *CVW 0.0 ******************************************************************** ** ROCK/FLUID PROPERTIES ******************************************************************** *ROCKFLUID **SORG *MATRIX *CON 0.4 **SORG *FRACTURE *CON 0.15 *RPT 1 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.0000 0.01 1.00 0.0010 0.0000 0.0 *SGT **SL KRG KROG PCGOD 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71 *RPT 2 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.000 0.01 1.00 0.001 0.00 0.0 *SGT **SNORM KRG KROG PCGOD 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25
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0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40 0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89 *RTYPE *MATRIX *CON 1 *RTYPE *FRACTURE *CON 2 ******************************************************************* ** INITIAL CONDITIONS ******************************************************************* *INITIAL *VERTICAL *BLOCK_CENTER *WATER_OIL_GAS **VERTICAL *OFF **PRES *MATRIX *CON 4000. **PRES *FRACTURE *CON 4000.0 **SO *MATRIX *CON .75 **SO *FRACTURE *CON 1.0 *PB *MATRIX *CON 300 *PB *FRACTURE *CON 300 *REFDEPTH 4000 *REFPRES 1080 *DWOC 30000. ** WOC out of system *DGOC 4035. ** GOC at the middle **CDEPTH 6500.0 ** In initialization all single phase blocks ** will be identified as oil-filled ********************************************************************* ** NUMERICAL CONTROL ********************************************************************* *NUMERICAL ** Simulator uses default timestep size control based ** on number of Newtonian iterations *DTMAX 5.0 *DTMIN 0.00001 *ITERMAX 100 *NORM *SATUR 0.05
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**SOLVER *PARASOL **PPATTERN 2 ******************************************************************** ** WELL DATA ******************************************************************** *RUN *DATE 2000 1 1 *DTWELL 0.00001 ** the firs time step *AIMSET *FRACTURE *CON 1 *AIMSET *MATRIX *CON 1 **WELLINIT *ITER *WELL 1 'INJ' *INJECTOR 1 *INCOMP *GAS *OPERATE *MAX *STG 10000.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 4:4 1.0 *OPEN *WELL 2 'PRO1' *PRODUCER 2 ** Define the type of well 1. *OPERATE *MAX *STO 15.0 *CONT *OPERATE *MIN *BHP 950.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERF *GEO 2 ** if jf kf wi 10 10 10:10 1.0 *OPEN *TIME 0.01 *TIME 0.1 *TIME 1 *TIME 10 *TIME 20 *TIME 30 *TIME 40 *TIME 50 *TIME 60 *TIME 70 *TIME 80 *TIME 90 *TIME 100 *TIME 120
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*TIME 130 *TIME 140 *TIME 150 *TIME 160 *TIME 170 *TIME 180 *TIME 190 *TIME 200 *TIME 210 *TIME 220 *TIME 230 *TIME 240 *TIME 250 *TIME 300 *TIME 350 *TIME 400 *TIME 450 *TIME 500 *TIME 550 *TIME 600 *TIME 650 *TIME 700 *TIME 750 *TIME 800 *TIME 850 *TIME 900 *TIME 950 *TIME 1000 *TIME 1050 *TIME 1100 *TIME 1150 *TIME 1200 *TIME 1250 *TIME 1300 *TIME 1350 *TIME 1400 *TIME 1450 *TIME 1500 *TIME 1550 *TIME 1600 *TIME 1650 *TIME 1700 *TIME 1750 *TIME 1800 *TIME 1850 *TIME 1900 *TIME 1950 *TIME 2000 *STOP
164
A.5 CMG-IMEX Input File for Discrete fracture model
**--------------------------------------------------------------------** ** GMcan001.DAT: Dual Porosity Model ** **--------------------------------------------------------------------** **--------------------------------------------------------------------** ** ** ** FILE: GMcant001.DAT ** ** ** ** MODEL: Fracture Gas Tracer Test ** ** DUAL POROSITY ** ** FIELD UNITS 3 COMPONENT FLUID ** ** ** **--------------------------------------------------------------------** ** ** ** ** **--------------------------------------------------------------------** ** CONTACT CMG at (403)531-1300 or [email protected] ** **--------------------------------------------------------------------** ************************************************************************ ** I/O Control Section ************************************************************************ *RESULTS *SIMULATOR *IMEX *TITLE1 ' GMcant002.DAT ' *TITLE2 ' Discrete fracture ' *TITLE3 ' FRACTURED RESERVOIR' *INUNIT *FIELD *WPRN *WELL 1 **write well result everey 10 time changes *WPRN *GRID 1 *WRST *TIME **write restart file **DIM *MDIMPL 100 *DIM *MDICLU 1200000 *OUTPRN *WELL *ALL *OUTPRN *RES *ALL **OUTPRN *TABLES *NONE *OUTPRN *GRID *SO SG PRES *WSRF *WELL *TIME **how frequency written to simulation result *WSRF *GRID *TIME **DIARY *CHANGES **IDENTIFY WHAT INFORMATION IS WRITTEN TO THE RESULT FILE *OUTSRF *WELL *OUTSRF *GRID *SG SO PRES
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*OUTSRF *RES *ALL ******************************************************************************** ** Reservoir Description Section ******************************************************************************** *GRID *cart 19 19 19 *KDIR *DOWN *DI *IVAR 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 *DJ *JVAR 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 *DK *KVAR 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 **DUALPOR **SUBDOMAIN **MINC 4 **SHAPE *GK *TRANSFER 3 **type of matrix-fracture model treat to phsaes *DEPTH 1 1 1 4000.00 ** Depth to center of first block, in bottom layer. *POR 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07
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19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08
167
0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07
168
19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 361*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08
169
0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 19*0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 0.08 0.07 *CPOR 4.5E-6 *PRPOR 1532 *PERMI 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2
170
361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000
171
0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 361*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 19*5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2 5000 0.2
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******************************************************************************** ** FLUID PROPERTIES ******************************************************************************** *MODEL *BLACKOIL *PVT *BG ** p rs bo Eg viso visg 500 100.000 1.137 0.002458 3.30 0.0145 2500 300.01 1.338 0.00145 2.40 0.0188 8000.0 1000.1 1.400 0.00043 2.00 0.0400 *DENSITY *OIL 52.6 *DENSITY *GAS 0.0615 *DENSITY *WATER 62.4 *CO 0.000E *CVO 0.0 *BWI 1.029 *CW 3.31E-6 *REFPW 1500 *VWI 0.5 *CVW 0.0 ******************************************************************************** ** ROCK/FLUID PROPERTIES ******************************************************************************** *ROCKFLUID **SORG *MATRIX *CON 0.4 **SORG *FRACTURE *CON 0.15 *RPT 1 **NTENA 0.178 NTENN 0.30 (1-2) *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.0000 0.01 1.00 0.0010 0.0000 0.0 *SGT **SL KRG KROG PCGOD 0.30 0.00 0.20 0.00 0.35 0.03 0.14 0.52 0.40 0.11 0.09 2.08 0.45 0.25 0.05 4.68 0.50 0.44 0.02 8.31 0.55 0.69 0.01 12.99 0.60 1.00 0.00 18.71 *RPT 2 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.000 0.01 1.00 0.001 0.00 0.0
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*SGT **SNORM KRG KROG PCGOD 0.10 0.00 1.00 0.00 0.15 0.00 0.87 0.00 0.20 0.02 0.75 0.02 0.25 0.04 0.64 0.04 0.30 0.07 0.54 0.06 0.35 0.11 0.44 0.10 0.40 0.16 0.36 0.14 0.45 0.22 0.28 0.19 0.50 0.28 0.22 0.25 0.55 0.36 0.16 0.32 0.60 0.44 0.11 0.40 0.65 0.54 0.07 0.48 0.70 0.64 0.04 0.57 0.75 0.75 0.02 0.67 0.80 0.87 0.00 0.78 0.85 1.00 0.00 0.89 *RTYPE *ALL 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2
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1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 361*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 19*2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
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******************************************************************************** ** INITIAL CONDITIONS ******************************************************************************** *INITIAL *VERTICAL *BLOCK_CENTER *WATER_OIL_GAS *PB *MATRIX *CON 300 *PB *FRACTURE *CON 300 *REFDEPTH 4000 *REFPRES 1080 *DWOC 30000. ** WOC out of system *DGOC 4038. ** GOC at the middle **CDEPTH 6500.0 ** In initialization all single phase blocks ** will be identified as oil-filled ******************************************************************************** ** NUMERICAL CONTROL ******************************************************************************** *NUMERICAL ** Simulator uses default timestep size control based ** on number of Newtonian iterations *DTMAX 0.1 *DTMIN 0.0000001 *ITERMAX 100 *NORM *SATUR 0.05 **SOLVER *PARASOL **PPATTERN 2 ******************************************************************************** ** WELL DATA ******************************************************************************** *RUN *DATE 2000 1 1 *DTWELL 0.000001 ** the firs time step *AIMSET *FRACTURE *CON 1 *AIMSET *MATRIX *CON 1
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**WELLINIT *ITER *WELL 1 'INJ' *INJECTOR 1 *INCOMP *GAS *OPERATE *MAX *STG 10000.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 6:7 1.0 *OPEN *WELL 2 'PRO1' *PRODUCER 2 ** Define the type of well 1. *OPERATE *MAX *STO 15.0 *CONT *OPERATE *MAX *STG 9900.0 *CONT *OPERATE *MIN *BHP 950.0 *CONT *GEOMETRY *K 0.5 0.25 1.0 0.0 *PERFRG *GEO 2 ** if jf kf wi 19 19 18:19 1.0 *OPEN *TIME 0.01 *TIME 0.1 *TIME 1 *TIME 10 *TIME 20 *TIME 30 *TIME 40 *TIME 50 *TIME 60 *TIME 70 *TIME 80 *TIME 90 *TIME 100 *TIME 120 *TIME 130 *TIME 140 *TIME 150 *TIME 160 *TIME 170 *TIME 180 *TIME 190 *TIME 200 *TIME 210 *TIME 220 *TIME 230 *TIME 240 *TIME 250 *TIME 300 *TIME 350 *TIME 400 *TIME 450 *TIME 500
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*TIME 550 *TIME 600 *TIME 650 *TIME 700 *TIME 750 *TIME 800 *TIME 850 *TIME 900 *TIME 950 *TIME 1000 *TIME 1050 *TIME 1100 *TIME 1150 *TIME 1200 *TIME 1250 *TIME 1300 *TIME 1350 *TIME 1400 *TIME 1450 *TIME 1500 *TIME 1550 *TIME 1600 *TIME 1650 *TIME 1700 *TIME 1750 *TIME 1800 *TIME 1850 *TIME 1900 *TIME 1950 *TIME 2000 *STOP
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A.6 CMG-GEM Input File for component tracking as tracer in Dual porosity
media
**--------------------------------------------------------------------** ** GMcan003.DAT: Compositional Dual Porosity Model ** **--------------------------------------------------------------------** **--------------------------------------------------------------------** ** ** ** FILE: GMcant003.DAT ** ** ** ** MODEL: Cantarell GAs tracer Test ** ** DUAL POROSITY ** ** FIELD UNITS 3 COMPONENT FLUID ** ** ** **--------------------------------------------------------------------** ** ** ** ** **--------------------------------------------------------------------** ** CONTACT CMG at (403)531-1300 or [email protected] ** **--------------------------------------------------------------------** ************************************************************************ ** I/O Control Section ************************************************************************ *RESULTS *SIMULATOR *GEM *TITLE1 ' GMcant003.DAT ' *TITLE2 ' Dual porosity ' *TITLE3 ' FRACTURED RESERVOIR' *INUNIT *FIELD *WPRN *WELL 1 **write well result everey 10 time changes *WPRN *GRID 1 *WRST *TIME **write restart file DIM *MDIMPL 100 DIM *MDICLU 200000 *OUTPRN *WELL *ALL *OUTPRN *RES *ALL **OUTPRN *TABLES *NONE *OUTPRN *GRID *SO SG Z 'N2A' Z 'N2B' X 'N2A' X 'N2B' Y 'N2A' Y 'N2B' *WSRF *WELL *TIME **how frequency written to simulation result *WSRF *GRID *TIME *DIARY *CHANGES **IDENTIFY WHAT INFORMATION IS WRITTEN TO THE RESULT FILE *OUTSRF *WELL *ZWEL 'N2A' 'PRO1' *ZWEL 'N2B' 'PRO1' *XWEL 'N2A' 'PRO1'
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*XWEL 'N2B' 'PRO1' *YWEL 'N2A' 'PRO1' *YWEL 'N2B' 'PRO1' *OUTSRF *GRID *SG SO PRES Z 'N2A' Z 'N2B' X 'N2A' X 'N2B' X 'N2B' Y 'N2A' Y 'N2B' *OUTSRF *RES *ALL *SUMMARY ************************************************************************** ** Reservoir Description Section ************************************************************************** *GRID *cart 10 10 10 *KDIR *DOWN *DUALPOR *DI *CON 100.0 *DJ *CON 100.0 *DK *CON 50.0 **SUBDOMAIN 3 **MINC 4 *SHAPE *GK *TRANSFER 3 **type of matrix-fracture model treat to phsaes *DIFRAC *CON 5 *DJFRAC *CON 5 *DKFRAC *CON 10 *DEPTH 1 1 1 4000.00 ** Depth to center of first block, in bottom layer. *POR *FRACTURE *CON 0.02 *POR *MATRIX *CON 0.070 *CPOR *FRACTURE 0.0E-6 *PRPOR *FRACTURE 4000.0 *DCPOR *FRACTURE 0.0 *CPOR *MATRIX 0.0E-6 *PRPOR *MATRIX 4000.0 *DCPOR *MATRIX 0.0 *PERMI *FRACTURE *CON 5000 *PERMJ *FRACTURE *CON 5000 *PERMK *FRACTURE *CON 5000 *PERMI *MATRIX *CON 0.2
183
*PERMJ *MATRIX *CON 0.2 *PERMK *MATRIX *CON 0.2 **************************************************************************** ** FLUID PROPERTIES **************************************************************************** *MODEL *PR *NC 7 7 *COMPNAME 'N2A' 'N2B' 'C1H2' 'C2C3' 'C4C5' 'C6P1' 'C7P2' *PCRIT 33.470 33.470 45.4 45.5 35.33 29.32 15 *TCRIT 126.11 126.11 190 331 441 507 788.5 *MW 28.010 28.01 16 36 64.7 86.18 323.8 *PCHOR 41.000 41.00 77 120.4 221.2 421.4 1196.75 *AC 0.0400 0.04 0.08 0.12 0.213 0.296 0.59 *ZCRIT 0.30 0.30 0.30 0.3 0.3 0.3 0.31 *HCFLAG 0 0 0 0 0 0 0 *OMEGA 0.45723 0.45723 0.45723 0.45723 0.457236 0.457236 0.457236 *OMEGB 0.077796 0.077796 0.077796 0.077796 0.077796 0.077796 0.077796 **BIN 0.1 ** 0.1877040 0.0027222 **OMEGAS 0.67000002 0.58495221 0.64649426 ** 0.45723552 0.45723552 **OMEGBS 0.03600000 0.11000001 0.08132145 ** 0.07779610 0.07779610 **BINS 0.0027123 ** 0.2907547 0.0027222 *PHASEID *DEN *TRES 121.0 *PSAT 300. *CW 3.0E-6 ** /PSI *DENW 63.648 ** LB/CU-FT *VISW 0.22 ***************************************************************************** ** ROCK/FLUID PROPERTIES ***************************************************************************** *ROCKFLUID *SIGMA *SORG *MATRIX *CON 0.4 *SORG *FRACTURE *CON 0.15 *RPT 1 **NTENA 0.178 NTENN 0.30 (1-2) *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 0.2000 0 1.00 0.0010 0.0000 0.0
184
*SGT **SL KRG KROG PCGOD 0.00 0.00 0.20 0.00 0.05 0.01 0.17 0.0 0.10 0.03 0.14 0.00 0.15 0.06 0.11 0.0 0.20 0.11 0.09 0.0 0.25 0.17 0.07 0.0 0.30 0.25 0.05 0.0 0.35 0.34 0.03 0.0 0.40 0.44 0.02 0.0 0.45 0.56 0.01 0.0 0.50 0.69 0.01 0.0 0.55 0.84 0.001 0.0 0.60 1.00 0.00 0.0 *RPT 2 *SWT **SNORM KRW NKRWO NPCWOD 0.00 0.000 1.000 0.0 1.00 0.001 0.00 0.0 *SGT **SNORM KRG KROG PCGOD 0.00 0.00 1.00 0.00 0.05 0.00 0.89 0.00 0.10 0.01 0.78 0.00 0.15 0.03 0.68 0.00 0.20 0.06 0.58 0.00 0.25 0.09 0.50 0.00 0.30 0.12 0.42 0.00 0.35 0.17 0.35 0.00 0.40 0.22 0.28 0.00 0.45 0.28 0.22 0.0 0.50 0.35 0.17 0.0 0.55 0.42 0.12 0.0 0.60 0.50 0.09 0.00 0.65 0.58 0.06 0.0 0.70 0.68 0.03 0.00 0.75 0.78 0.01 0.00 0.80 0.89 0.001 0.00 0.85 1.00 0.00 0.00 *RTYPE *MATRIX *CON 1 *RTYPE *FRACTURE *CON 2 ****************************************************************************** ** INITIAL CONDITIONS ******************************************************************************
185
*INITIAL *VERTICAL *BLOCK_CENTER *WATER_OIL_GAS *REFDEPTH 4000 *REFPRES 1080 *DWOC 30000. ** WOC out of system *DGOC 4175. ** GOC at the middle *ZOIL 0.000 0.00 0.1747 0.1415 0.0970 0.037 0.5498 *ZGAS 0.0 0.000 0.90 0.1 0 0 0 **CDEPTH 6500.0 ** In initialization all single phase blocks ** will be identified as oil-filled ******************************************************************************* ** NUMERICAL CONTROL ******************************************************************************* *NUMERICAL ** Simulator uses default timestep size control based ** on number of Newtonian iterations *DTMAX 1.00 *DTMIN 0.0001 *ITERMAX 50 *NEWTONCYC 25 **PRECC 0.0005 **NORM *SATUR 0.05 *MAXCHANGE *GMOLAR 0.80 **SOLVER *PARASOL **PPATTERN 2 ******************************************************************************* ** WELL DATA ******************************************************************************* *RUN *DATE 2000 1 1 *DTWELL 0.001 ** the firs time step *AIMSET *FRACTURE *CON 1
186
*AIMSET *MATRIX *CON 1 **WELLINIT *ITER *WELL 1 'INJ' *INJECTOR 1 *INCOMP *SOLVENT 0.95 0.050 0.0 0 0 0 0 *OPERATE *MAX *STG 3000000.0 *CONT *GEOMETRY *K 0.5 0.64 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 3:4 1.0 *OPEN *WELL 2 'PRO1' *PRODUCER 2 ** Define the type of well 1. *OPERATE *MAX *STO 5000.0 *CONT *OPERATE *MAX *STG 3000000.0 *CONT *OPERATE *MIN *BHP 800.0 *CONT *GEOMETRY *K 0.5 0.64 1.0 0.0 *PERF *GEO 2 ** if jf kf wi 10 10 10:10 1.0 *OPEN *TIME 0.01 *TIME 0.1 *TIME 1 *TIME 5 *TIME 10 *TIME 15 *TIME 20 *TIME 25 *TIME 30 *TIME 35 *TIME 40 *TIME 45 *TIME 50 *TIME 55 *TIME 60 *TIME 65 *TIME 70 *TIME 75 *TIME 80 *TIME 85 *TIME 90 *TIME 95 *TIME 100 *TIME 105 *TIME 110 *TIME 115 *TIME 120 *TIME 125 *TIME 130 *TIME 135
187
*TIME 140 *TIME 145 *TIME 150 *WELL 1 'INJ' *INJECTOR 1 *INCOMP *SOLVENT 1.0 0.0 0.0 0 0 0 0 *OPERATE *MAX *STG 5000000.0 *CONT *GEOMETRY *K 0.5 0.64 1.0 0.0 *PERF *GEO 1 ** if jf kf wi 1 1 3:4 1.0 *OPEN *TIME 155 *TIME 160 *TIME 165 *TIME 170 *TIME 175 *TIME 180 *TIME 185 *TIME 190 *TIME 195 *TIME 200 *TIME 205 *TIME 210 *TIME 215 *TIME 220 *TIME 225 *TIME 230 *TIME 235 *TIME 240 *TIME 245 *TIME 250 *TIME 255 *TIME 260 *TIME 265 *TIME 270 *TIME 275 *TIME 280 *TIME 285 *TIME 290 *TIME 295 *TIME 300 *TIME 310 *TIME 320 *TIME 330 *TIME 340 *TIME 350 *TIME 360 *TIME 370 *TIME 380 *TIME 390 *TIME 400 *TIME 410
188
*TIME 420 *TIME 430 *TIME 440 *TIME 450 *TIME 460 *TIME 470 *TIME 480 *TIME 490 *TIME 500 *TIME 520 *TIME 540 *TIME 560 *TIME 580 *TIME 600 *TIME 620 *TIME 640 *TIME 660 *TIME 680 *TIME 700 *TIME 720 *TIME 740 *TIME 760 *TIME 780 *TIME 800 *TIME 820 *TIME 840 *TIME 860 *TIME 880 *TIME 900 *TIME 920 *TIME 940 *TIME 960 *TIME 980 *TIME 1000 *TIME 1050 *TIME 1100 *TIME 1150 *TIME 1200 *TIME 1250 *TIME 1300 *TIME 1350 *TIME 1400 *TIME 1450 *TIME 1500 *TIME 1550 *TIME 1600 *TIME 1650 *TIME 1700 *TIME 1750 *TIME 1800 *TIME 1850 *TIME 1900 *TIME 1950 *TIME 2000 *STOP
189
Nomenclature
b = Half thickness of fracture aperture
)t,x(C0 = Initial tracer concentration of the model
gIiC = Initial concentration of component i in gas
fiC = Concentration of tracer i in the fracture
fijC = Concentration of component i in phase j in the fracture
iC = Total concentration of tracer i
igC = Concentration of tracer i in the gas phase
ioC = Concentration of tracer i in the oil phase
iwC = Concentration of the tracer i in water phase
ijC = Concentration of the tracer i in phase j
iJC = Initial concentration of tracer i
itC = Total tracer concentrations for tracer i
miC = Concentration of tracer i in the matrix
mijC = Concentration of tracer i in phase j in the matrix
nC = Concentration of the conservative tracer
maxnC = Maximum concentration of the conservative
190
oIiC = Initial concentration of component i in oil
pC = Concentration of the partitioning tracer
pcjC = End point capillary pressure for phase j
maxpC = Maximum concentration of the partitioning
wIiC = Initial concentration of component i in water
je = relative permeability exponent of phase j
jf = Fractional flow of phase j
h = Reservoir thickness
fk = Fracture permeability
iK = Partition coefficient of tracer i
ijKrr
= Dispersion coefficient of component i in phase
mk = Matrix permeability
tiK = Partition coefficient of tracer i
rjk = Relative permeability of phase j
orjk = End point relative permeability of phase j
xk = Permeability in the x direction
yk = Permeability in the y direction
zk = Permeability in the z direction
191
L = Reservoir length
xL = Length of the matrix block in x direction
yL = Length of the matrix block in the y direction
zL = Length of the matrix block in the z direction
m = Mass of the tracer produced at a given producer
i0m = Zeroth temporal moment for tracer i
ig0m = Zeroth temporal moment for tracer i in gas phase
i1m = first temporal moment for tracer i
M = Total mass of the tracer injected
pcjn = capillary pressure exponent of phase j
fiNr
= Flux of tracer I in fracture
gN = Gravity number
iNr
= Flux of tracer i
cP = Capillary pressure
fP = Fracture Pressure
mP = Matrix Pressure
injq = Injection rate
oq = Oil flow rate
Q = Total injection rate
192
fiR = Retardation factor of tracer i
LR = Effective length to thickness ratio
)x(S0 = Initial slowness of the model
*S = Saturation value at zero capillary pressure
gS = Gas Saturation
gS = Average gas saturation
grS = Residual gas saturation
jS = Saturation of phase j
jrS = Residual saturation of phase j
njS = Normalized saturation of phase j
oS = Oil saturation
oS = Average oil saturation
orS = Average residual oil saturation
wS = Aqueous phase saturation
t = Time
Dt = Characteristic dimensionless time
*Dt = Characteristic dimensionless time for constant shape factor
Dt = dimensionless mean residence time
193
Dft = Dimensionless fracture mean residence time
Dmt = Dimensionless matrix mean residence time
ft = Fracture mean residence time
it = Mean residence time of tracer i
mt = Matrix mean residence time
slugt = Tracer slug time
u = Fluid velocity into the reservoir
jur = Flux of phase j
BV = Bulk volume of the reservoir
cV = Mean residence volume of the conservative tracer
iV = Mean residence volume of tracer i
pV = Mean Residence Volume of the partitioning tracer
sV = Swept pore volume
slugV = Volume of the tracer slug
ix = Mole fraction of tracer i in liquid phase
iy = Mole fraction of tracer i in gaseous phase
194
Greek Symbols
φ = Porosity
fφ = fracture porosity
mφ = matrix porosity
σ = Shape Factor
µ = Viscosity of the fluid
τ = Transit time for the partitioning tracer
fmτ = Transfer function
oρ = Oil density
gρ = gas density
195
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VITA
Gholamreza Garmeh was born in Bojnourd, Iran on Apirl 9, 1980, son of Mr. R.
Garmeh and Mrs. R. Garmeh. After completing his high school education at I.H.M.
pre-university, Bojnourd, Iran, in 1998, he entered the Petroleum University of
Technology, Ahwaz, Iran. He received the degree of Bachelor of Science in
Petroleum Engineering from P.U.T, Ahwaz, Iran, in May 2002. In September 2003,
he entered The Graduate School at The University of Texas at Austin.
Permanent Address: 12 Summar ave. 17 Shahrivar st.
Bojnourd, 94519
Iran
This thesis was typed by the author.